diff --git a/doc/source/release.rst b/doc/source/release.rst
index 8de8929c5fa7a..0666eb7f88675 100644
--- a/doc/source/release.rst
+++ b/doc/source/release.rst
@@ -111,6 +111,7 @@ Bug Fixes
   - Bug in ``pd.read_msgpack`` with inferring a ``DateTimeIndex`` frequencey
     incorrectly (:issue:`5947`)
   - Fixed ``to_datetime`` for array with both Tz-aware datetimes and ``NaT``s  (:issue:`5961`)
+  - Bug in rolling skew/kurtosis when passed a Series with bad data (:issue:`5749`)
 
 pandas 0.13.0
 -------------
diff --git a/pandas/algos.pyx b/pandas/algos.pyx
index 08ec707b0d96d..d916de32b7cd3 100644
--- a/pandas/algos.pyx
+++ b/pandas/algos.pyx
@@ -1167,8 +1167,11 @@ def roll_skew(ndarray[double_t] input, int win, int minp):
 
             R = sqrt(B)
 
-            output[i] = ((sqrt(nobs * (nobs - 1.)) * C) /
-                         ((nobs-2) * R * R * R))
+            if B == 0 or nobs < 3:
+                output[i] = NaN
+            else:
+                output[i] = ((sqrt(nobs * (nobs - 1.)) * C) /
+                             ((nobs-2) * R * R * R))
         else:
             output[i] = NaN
 
@@ -1236,10 +1239,15 @@ def roll_kurt(ndarray[double_t] input,
             R = R * A
             D = xxxx / nobs - R - 6*B*A*A - 4*C*A
 
-            K = (nobs * nobs - 1.)*D/(B*B) - 3*((nobs-1.)**2)
-            K = K / ((nobs - 2.)*(nobs-3.))
+            if B == 0 or nobs < 4:
+                output[i] = NaN
+
+            else:
+                K = (nobs * nobs - 1.)*D/(B*B) - 3*((nobs-1.)**2)
+                K = K / ((nobs - 2.)*(nobs-3.))
+
+                output[i] = K
 
-            output[i] = K
         else:
             output[i] = NaN
 
diff --git a/pandas/stats/tests/test_moments.py b/pandas/stats/tests/test_moments.py
index 7381d4c1ae0b4..970adeace1e0f 100644
--- a/pandas/stats/tests/test_moments.py
+++ b/pandas/stats/tests/test_moments.py
@@ -741,6 +741,50 @@ def test_expanding_corr_pairwise(self):
         for i in result.items:
             assert_almost_equal(result[i], rolling_result[i])
 
+    def test_rolling_skew_edge_cases(self):
+
+        all_nan = Series([np.NaN] * 5)
+
+        # yields all NaN (0 variance)
+        d = Series([1] * 5)
+        x = mom.rolling_skew(d, window=5)
+        assert_series_equal(all_nan, x)
+
+        # yields all NaN (window too small)
+        d = Series(np.random.randn(5))
+        x = mom.rolling_skew(d, window=2)
+        assert_series_equal(all_nan, x)
+
+        # yields [NaN, NaN, NaN, 0.177994, 1.548824]
+        d = Series([-1.50837035, -0.1297039 ,  0.19501095,
+                       1.73508164,  0.41941401])
+        expected = Series([np.NaN, np.NaN, np.NaN,
+                              0.177994, 1.548824])
+        x = mom.rolling_skew(d, window=4)
+        assert_series_equal(expected, x)
+
+    def test_rolling_kurt_edge_cases(self):
+
+        all_nan = Series([np.NaN] * 5)
+
+        # yields all NaN (0 variance)
+        d = Series([1] * 5)
+        x = mom.rolling_kurt(d, window=5)
+        assert_series_equal(all_nan, x)
+
+        # yields all NaN (window too small)
+        d = Series(np.random.randn(5))
+        x = mom.rolling_kurt(d, window=3)
+        assert_series_equal(all_nan, x)
+
+        # yields [NaN, NaN, NaN, 1.224307, 2.671499]
+        d = Series([-1.50837035, -0.1297039 ,  0.19501095,
+                    1.73508164,  0.41941401])
+        expected = Series([np.NaN, np.NaN, np.NaN,
+                           1.224307, 2.671499])
+        x = mom.rolling_kurt(d, window=4)
+        assert_series_equal(expected, x)
+
     def _check_expanding_ndarray(self, func, static_comp, has_min_periods=True,
                                  has_time_rule=True, preserve_nan=True):
         result = func(self.arr)