diff --git a/doc/whats_new/v0.11.rst b/doc/whats_new/v0.11.rst
index a6cb21821..8e54a275b 100644
--- a/doc/whats_new/v0.11.rst
+++ b/doc/whats_new/v0.11.rst
@@ -43,3 +43,8 @@ Enhancements
   parameters. A new fitted parameter `categorical_encoder_` is exposed to access the
   fitted encoder.
   :pr:`1001` by :user:`Guillaume Lemaitre <glemaitre>`.
+
+- :class:`~imblearn.under_sampling.RandomUnderSampler` and
+  :class:`~imblearn.over_sampling.RandomOverSampler` (when `shrinkage is not
+  None`) now accept any data types and will not attempt any data conversion.
+  :pr:`1004` by :user:`Guillaume Lemaitre <glemaitre>`.
diff --git a/examples/api/plot_sampling_strategy_usage.py b/examples/api/plot_sampling_strategy_usage.py
index b739a41c6..dbb52fcdf 100644
--- a/examples/api/plot_sampling_strategy_usage.py
+++ b/examples/api/plot_sampling_strategy_usage.py
@@ -59,10 +59,9 @@
 # resampling and the number of samples in the minority class, respectively.
 
 # %%
-import numpy as np
 
 # select only 2 classes since the ratio make sense in this case
-binary_mask = np.bitwise_or(y == 0, y == 2)
+binary_mask = y.isin([0, 1])
 binary_y = y[binary_mask]
 binary_X = X[binary_mask]
 
diff --git a/imblearn/datasets/tests/test_imbalance.py b/imblearn/datasets/tests/test_imbalance.py
index 2d8e278fa..ac3b417c7 100644
--- a/imblearn/datasets/tests/test_imbalance.py
+++ b/imblearn/datasets/tests/test_imbalance.py
@@ -67,11 +67,14 @@ def test_make_imbalance_dict(iris, sampling_strategy, expected_counts):
     ],
 )
 def test_make_imbalanced_iris(as_frame, sampling_strategy, expected_counts):
-    pytest.importorskip("pandas")
-    iris = load_iris(as_frame=True)
+    pd = pytest.importorskip("pandas")
+    iris = load_iris(as_frame=as_frame)
     X, y = iris.data, iris.target
     y = iris.target_names[iris.target]
+    if as_frame:
+        y = pd.Series(iris.target_names[iris.target], name="target")
     X_res, y_res = make_imbalance(X, y, sampling_strategy=sampling_strategy)
     if as_frame:
         assert hasattr(X_res, "loc")
+        pd.testing.assert_index_equal(X_res.index, y_res.index)
     assert Counter(y_res) == expected_counts
diff --git a/imblearn/ensemble/tests/test_bagging.py b/imblearn/ensemble/tests/test_bagging.py
index 1f1d408ef..01532add8 100644
--- a/imblearn/ensemble/tests/test_bagging.py
+++ b/imblearn/ensemble/tests/test_bagging.py
@@ -572,11 +572,12 @@ def roughly_balanced_bagging(X, y, replace=False):
 
     # Roughly Balanced Bagging
     rbb = BalancedBaggingClassifier(
-        estimator=CountDecisionTreeClassifier(),
+        estimator=CountDecisionTreeClassifier(random_state=0),
         n_estimators=2,
         sampler=FunctionSampler(
             func=roughly_balanced_bagging, kw_args={"replace": replace}
         ),
+        random_state=0,
     )
     rbb.fit(X, y)
 
diff --git a/imblearn/over_sampling/_random_over_sampler.py b/imblearn/over_sampling/_random_over_sampler.py
index 7175855ea..63b5a66a7 100644
--- a/imblearn/over_sampling/_random_over_sampler.py
+++ b/imblearn/over_sampling/_random_over_sampler.py
@@ -15,6 +15,7 @@
 from ..utils import Substitution, check_target_type
 from ..utils._docstring import _random_state_docstring
 from ..utils._param_validation import Interval
+from ..utils._validation import _check_X
 from .base import BaseOverSampler
 
 
@@ -154,14 +155,9 @@ def __init__(
 
     def _check_X_y(self, X, y):
         y, binarize_y = check_target_type(y, indicate_one_vs_all=True)
-        X, y = self._validate_data(
-            X,
-            y,
-            reset=True,
-            accept_sparse=["csr", "csc"],
-            dtype=None,
-            force_all_finite=False,
-        )
+        X = _check_X(X)
+        self._check_n_features(X, reset=True)
+        self._check_feature_names(X, reset=True)
         return X, y, binarize_y
 
     def _fit_resample(self, X, y):
@@ -258,4 +254,7 @@ def _more_tags(self):
             "X_types": ["2darray", "string", "sparse", "dataframe"],
             "sample_indices": True,
             "allow_nan": True,
+            "_xfail_checks": {
+                "check_complex_data": "Robust to this type of data.",
+            },
         }
diff --git a/imblearn/over_sampling/_smote/base.py b/imblearn/over_sampling/_smote/base.py
index da880f87c..f26b91b19 100644
--- a/imblearn/over_sampling/_smote/base.py
+++ b/imblearn/over_sampling/_smote/base.py
@@ -27,6 +27,7 @@
 from ...utils import Substitution, check_neighbors_object, check_target_type
 from ...utils._docstring import _n_jobs_docstring, _random_state_docstring
 from ...utils._param_validation import HasMethods, Interval
+from ...utils._validation import _check_X
 from ...utils.fixes import _mode
 from ..base import BaseOverSampler
 
@@ -559,9 +560,9 @@ def _check_X_y(self, X, y):
         features.
         """
         y, binarize_y = check_target_type(y, indicate_one_vs_all=True)
-        if not (hasattr(X, "__array__") or sparse.issparse(X)):
-            X = check_array(X, dtype=object)
+        X = _check_X(X)
         self._check_n_features(X, reset=True)
+        self._check_feature_names(X, reset=True)
         return X, y, binarize_y
 
     def _validate_estimator(self):
diff --git a/imblearn/over_sampling/tests/test_random_over_sampler.py b/imblearn/over_sampling/tests/test_random_over_sampler.py
index b72132d19..6ad4b75ef 100644
--- a/imblearn/over_sampling/tests/test_random_over_sampler.py
+++ b/imblearn/over_sampling/tests/test_random_over_sampler.py
@@ -4,6 +4,7 @@
 # License: MIT
 
 from collections import Counter
+from datetime import datetime
 
 import numpy as np
 import pytest
@@ -273,3 +274,16 @@ def test_random_over_sampler_strings(sampling_strategy):
         random_state=0,
     )
     RandomOverSampler(sampling_strategy=sampling_strategy).fit_resample(X, y)
+
+
+def test_random_over_sampling_datetime():
+    """Check that we don't convert input data and only sample from it."""
+    pd = pytest.importorskip("pandas")
+    X = pd.DataFrame({"label": [0, 0, 0, 1], "td": [datetime.now()] * 4})
+    y = X["label"]
+    ros = RandomOverSampler(random_state=0)
+    X_res, y_res = ros.fit_resample(X, y)
+
+    pd.testing.assert_series_equal(X_res.dtypes, X.dtypes)
+    pd.testing.assert_index_equal(X_res.index, y_res.index)
+    assert_array_equal(y_res.to_numpy(), np.array([0, 0, 0, 1, 1, 1]))
diff --git a/imblearn/under_sampling/_prototype_selection/_random_under_sampler.py b/imblearn/under_sampling/_prototype_selection/_random_under_sampler.py
index ed47fe586..876195a6d 100644
--- a/imblearn/under_sampling/_prototype_selection/_random_under_sampler.py
+++ b/imblearn/under_sampling/_prototype_selection/_random_under_sampler.py
@@ -9,6 +9,7 @@
 
 from ...utils import Substitution, check_target_type
 from ...utils._docstring import _random_state_docstring
+from ...utils._validation import _check_X
 from ..base import BaseUnderSampler
 
 
@@ -97,14 +98,9 @@ def __init__(
 
     def _check_X_y(self, X, y):
         y, binarize_y = check_target_type(y, indicate_one_vs_all=True)
-        X, y = self._validate_data(
-            X,
-            y,
-            reset=True,
-            accept_sparse=["csr", "csc"],
-            dtype=None,
-            force_all_finite=False,
-        )
+        X = _check_X(X)
+        self._check_n_features(X, reset=True)
+        self._check_feature_names(X, reset=True)
         return X, y, binarize_y
 
     def _fit_resample(self, X, y):
@@ -140,4 +136,7 @@ def _more_tags(self):
             "X_types": ["2darray", "string", "sparse", "dataframe"],
             "sample_indices": True,
             "allow_nan": True,
+            "_xfail_checks": {
+                "check_complex_data": "Robust to this type of data.",
+            },
         }
diff --git a/imblearn/under_sampling/_prototype_selection/tests/test_random_under_sampler.py b/imblearn/under_sampling/_prototype_selection/tests/test_random_under_sampler.py
index bcb8682e2..9fc9f084c 100644
--- a/imblearn/under_sampling/_prototype_selection/tests/test_random_under_sampler.py
+++ b/imblearn/under_sampling/_prototype_selection/tests/test_random_under_sampler.py
@@ -4,6 +4,7 @@
 # License: MIT
 
 from collections import Counter
+from datetime import datetime
 
 import numpy as np
 import pytest
@@ -148,3 +149,16 @@ def test_random_under_sampler_strings(sampling_strategy):
         random_state=0,
     )
     RandomUnderSampler(sampling_strategy=sampling_strategy).fit_resample(X, y)
+
+
+def test_random_under_sampling_datetime():
+    """Check that we don't convert input data and only sample from it."""
+    pd = pytest.importorskip("pandas")
+    X = pd.DataFrame({"label": [0, 0, 0, 1], "td": [datetime.now()] * 4})
+    y = X["label"]
+    rus = RandomUnderSampler(random_state=0)
+    X_res, y_res = rus.fit_resample(X, y)
+
+    pd.testing.assert_series_equal(X_res.dtypes, X.dtypes)
+    pd.testing.assert_index_equal(X_res.index, y_res.index)
+    assert_array_equal(y_res.to_numpy(), np.array([0, 1]))
diff --git a/imblearn/utils/_validation.py b/imblearn/utils/_validation.py
index b8df4b926..da1e492f4 100644
--- a/imblearn/utils/_validation.py
+++ b/imblearn/utils/_validation.py
@@ -12,8 +12,11 @@
 import numpy as np
 from sklearn.base import clone
 from sklearn.neighbors import NearestNeighbors
-from sklearn.utils import column_or_1d
+from sklearn.utils import check_array, column_or_1d
 from sklearn.utils.multiclass import type_of_target
+from sklearn.utils.validation import _num_samples
+
+from .fixes import _is_pandas_df
 
 SAMPLING_KIND = (
     "over-sampling",
@@ -35,6 +38,12 @@ def __init__(self, X, y):
     def transform(self, X, y):
         X = self._transfrom_one(X, self.x_props)
         y = self._transfrom_one(y, self.y_props)
+        if self.x_props["type"].lower() == "dataframe" and self.y_props[
+            "type"
+        ].lower() in {"series", "dataframe"}:
+            # We lost the y.index during resampling. We can safely use X.index to align
+            # them.
+            y.index = X.index
         return X, y
 
     def _gets_props(self, array):
@@ -607,3 +616,18 @@ def inner_f(*args, **kwargs):
         return f(**kwargs)
 
     return inner_f
+
+
+def _check_X(X):
+    """Check X and do not check it if a dataframe."""
+    n_samples = _num_samples(X)
+    if n_samples < 1:
+        raise ValueError(
+            f"Found array with {n_samples} sample(s) while a minimum of 1 is "
+            "required."
+        )
+    if _is_pandas_df(X):
+        return X
+    return check_array(
+        X, dtype=None, accept_sparse=["csr", "csc"], force_all_finite=False
+    )
diff --git a/imblearn/utils/fixes.py b/imblearn/utils/fixes.py
index 1868cb1fd..023d8a152 100644
--- a/imblearn/utils/fixes.py
+++ b/imblearn/utils/fixes.py
@@ -5,6 +5,7 @@
 which the fix is no longer needed.
 """
 import functools
+import sys
 
 import numpy as np
 import scipy
@@ -132,3 +133,18 @@ def _is_fitted(estimator, attributes=None, all_or_any=all):
 
 else:
     from sklearn.utils.validation import _is_fitted  # type: ignore[no-redef]
+
+try:
+    from sklearn.utils.validation import _is_pandas_df
+except ImportError:
+
+    def _is_pandas_df(X):
+        """Return True if the X is a pandas dataframe."""
+        if hasattr(X, "columns") and hasattr(X, "iloc"):
+            # Likely a pandas DataFrame, we explicitly check the type to confirm.
+            try:
+                pd = sys.modules["pandas"]
+            except KeyError:
+                return False
+            return isinstance(X, pd.DataFrame)
+        return False