diff --git a/xarray/backends/api.py b/xarray/backends/api.py
index c7481e22b59..a489e681aff 100644
--- a/xarray/backends/api.py
+++ b/xarray/backends/api.py
@@ -951,12 +951,18 @@ def open_mfdataset(
                 coords=coords,
                 ids=ids,
                 join=join,
+                combine_attrs="drop",
             )
         elif combine == "by_coords":
             # Redo ordering from coordinates, ignoring how they were ordered
             # previously
             combined = combine_by_coords(
-                datasets, compat=compat, data_vars=data_vars, coords=coords, join=join
+                datasets,
+                compat=compat,
+                data_vars=data_vars,
+                coords=coords,
+                join=join,
+                combine_attrs="drop",
             )
         else:
             raise ValueError(
diff --git a/xarray/tests/test_backends.py b/xarray/tests/test_backends.py
index 916c29ba7bd..72c1d740e55 100644
--- a/xarray/tests/test_backends.py
+++ b/xarray/tests/test_backends.py
@@ -2652,6 +2652,36 @@ def test_open_mfdataset_does_same_as_concat(self, combine, opt, join):
                 ds_expect = xr.concat([ds1, ds2], data_vars=opt, dim="t", join=join)
                 assert_identical(ds, ds_expect)
 
+    def test_open_mfdataset_dataset_attr_by_coords(self):
+        """
+        Case when an attribute differs across the multiple files
+        """
+        with self.setup_files_and_datasets() as (files, [ds1, ds2]):
+            # Give the files an inconsistent attribute
+            for i, f in enumerate(files):
+                ds = open_dataset(f).load()
+                ds.attrs["test_dataset_attr"] = 10 + i
+                ds.close()
+                ds.to_netcdf(f)
+
+            with xr.open_mfdataset(files, combine="by_coords", concat_dim="t") as ds:
+                assert ds.test_dataset_attr == 10
+
+    def test_open_mfdataset_dataarray_attr_by_coords(self):
+        """
+        Case when an attribute of a member DataArray differs across the multiple files
+        """
+        with self.setup_files_and_datasets() as (files, [ds1, ds2]):
+            # Give the files an inconsistent attribute
+            for i, f in enumerate(files):
+                ds = open_dataset(f).load()
+                ds["v1"].attrs["test_dataarray_attr"] = i
+                ds.close()
+                ds.to_netcdf(f)
+
+            with xr.open_mfdataset(files, combine="by_coords", concat_dim="t") as ds:
+                assert ds["v1"].test_dataarray_attr == 0
+
     @pytest.mark.parametrize("combine", ["nested", "by_coords"])
     @pytest.mark.parametrize("opt", ["all", "minimal", "different"])
     def test_open_mfdataset_exact_join_raises_error(self, combine, opt):
diff --git a/xarray/tests/test_concat.py b/xarray/tests/test_concat.py
index e5038dd4af2..41a62dd67d0 100644
--- a/xarray/tests/test_concat.py
+++ b/xarray/tests/test_concat.py
@@ -278,6 +278,35 @@ def test_concat_combine_attrs_kwarg(self):
             actual = concat([ds1, ds2], dim="x", combine_attrs=combine_attrs)
             assert_identical(actual, expected[combine_attrs])
 
+    def test_concat_combine_attrs_kwarg_member_attrs(self):
+        ds1 = Dataset({"a": ("x", [0])}, coords={"x": [0]})
+        ds1["a"].attrs = {"b": 42}
+
+        ds2 = Dataset({"a": ("x", [0])}, coords={"x": [1]})
+        ds2["a"].attrs = {"b": 42, "c": 43}
+
+        expected = {}
+
+        expected["drop"] = Dataset({"a": ("x", [0, 0])}, {"x": [0, 1]})
+
+        expected["no_conflicts"] = Dataset({"a": ("x", [0, 0])}, {"x": [0, 1]})
+        expected["no_conflicts"]["a"].attrs = {"b": 42, "c": 43}
+
+        expected["override"] = Dataset({"a": ("x", [0, 0])}, {"x": [0, 1]})
+        expected["override"]["a"].attrs = {"b": 42}
+
+        with raises_regex(ValueError, "combine_attrs='identical'"):
+            actual = concat([ds1, ds2], dim="x", combine_attrs="identical")
+        with raises_regex(ValueError, "combine_attrs='no_conflicts'"):
+            ds3 = ds2.copy(deep=True)
+            ds3["a"].attrs["b"] = 44
+            actual = concat([ds1, ds3], dim="x", combine_attrs="no_conflicts")
+
+        for combine_attrs in expected:
+            actual = concat([ds1, ds2], dim="x", combine_attrs=combine_attrs)
+            assert_identical(actual, expected[combine_attrs])
+            assert_identical(actual["a"], expected[combine_attrs]["a"])
+
     def test_concat_promote_shape(self):
         # mixed dims within variables
         objs = [Dataset({}, {"x": 0}), Dataset({"x": [1]})]