diff --git a/doc/source/v0.14.1.txt b/doc/source/v0.14.1.txt
index 0aa30e536ef48..ef8de452d1d38 100644
--- a/doc/source/v0.14.1.txt
+++ b/doc/source/v0.14.1.txt
@@ -65,3 +65,4 @@ There are no experimental changes in 0.14.1
 Bug Fixes
 ~~~~~~~~~
 
+- Bug in ``Index.min`` and ``max`` doesn't handle ``nan`` and ``NaT`` properly (:issue:`7261`)
diff --git a/pandas/core/base.py b/pandas/core/base.py
index 0e7bc0fee8a48..6bbcc33c2271b 100644
--- a/pandas/core/base.py
+++ b/pandas/core/base.py
@@ -236,11 +236,13 @@ def _wrap_access_object(self, obj):
 
     def max(self):
         """ The maximum value of the object """
-        return self.values.max()
+        import pandas.core.nanops
+        return pandas.core.nanops.nanmax(self.values)
 
     def min(self):
         """ The minimum value of the object """
-        return self.values.min()
+        import pandas.core.nanops
+        return pandas.core.nanops.nanmin(self.values)
 
     def value_counts(self, normalize=False, sort=True, ascending=False,
                      bins=None):
diff --git a/pandas/tests/test_base.py b/pandas/tests/test_base.py
index 927e096f8d769..4aaab3b2c52a5 100644
--- a/pandas/tests/test_base.py
+++ b/pandas/tests/test_base.py
@@ -1,5 +1,5 @@
 import re
-from datetime import timedelta
+from datetime import datetime, timedelta
 import numpy as np
 import pandas.compat as compat
 import pandas as pd
@@ -210,6 +210,39 @@ def test_ops(self):
                     expected = expected.astype('M8[ns]').astype('int64')
                     self.assertEqual(result.value, expected)
 
+    def test_nanops(self):
+        # GH 7261
+        for op in ['max','min']:
+            for klass in [Index, Series]:
+
+                obj = klass([np.nan, 2.0])
+                self.assertEqual(getattr(obj, op)(), 2.0)
+
+                obj = klass([np.nan])
+                self.assertTrue(pd.isnull(getattr(obj, op)()))
+
+                obj = klass([])
+                self.assertTrue(pd.isnull(getattr(obj, op)()))
+
+                obj = klass([pd.NaT, datetime(2011, 11, 1)])
+                # check DatetimeIndex monotonic path
+                self.assertEqual(getattr(obj, op)(), datetime(2011, 11, 1))
+
+                obj = klass([pd.NaT, datetime(2011, 11, 1), pd.NaT])
+                # check DatetimeIndex non-monotonic path
+                self.assertEqual(getattr(obj, op)(), datetime(2011, 11, 1))
+
+            # explicitly create DatetimeIndex
+            obj = DatetimeIndex([])
+            self.assertTrue(pd.isnull(getattr(obj, op)()))
+
+            obj = DatetimeIndex([pd.NaT])
+            self.assertTrue(pd.isnull(getattr(obj, op)()))
+
+            obj = DatetimeIndex([pd.NaT, pd.NaT, pd.NaT])
+            self.assertTrue(pd.isnull(getattr(obj, op)()))
+
+
     def test_value_counts_unique_nunique(self):
         for o in self.objs:
             klass = type(o)
diff --git a/pandas/tseries/index.py b/pandas/tseries/index.py
index 0e18509d9bc26..d83022c814d0a 100644
--- a/pandas/tseries/index.py
+++ b/pandas/tseries/index.py
@@ -1758,20 +1758,28 @@ def min(self, axis=None):
         """
         Overridden ndarray.min to return a Timestamp
         """
-        if self.is_monotonic:
-            return self[0]
+        mask = self.asi8 == tslib.iNaT
+        masked = self[~mask]
+        if len(masked) == 0:
+            return tslib.NaT
+        elif self.is_monotonic:
+            return masked[0]
         else:
-            min_stamp = self.asi8.min()
+            min_stamp = masked.asi8.min()
             return Timestamp(min_stamp, tz=self.tz)
 
     def max(self, axis=None):
         """
         Overridden ndarray.max to return a Timestamp
         """
-        if self.is_monotonic:
-            return self[-1]
+        mask = self.asi8 == tslib.iNaT
+        masked = self[~mask]
+        if len(masked) == 0:
+            return tslib.NaT
+        elif self.is_monotonic:
+            return masked[-1]
         else:
-            max_stamp = self.asi8.max()
+            max_stamp = masked.asi8.max()
             return Timestamp(max_stamp, tz=self.tz)
 
     def to_julian_date(self):