diff --git a/elephant/spike_train_dissimilarity.py b/elephant/spike_train_dissimilarity.py
index 3234f8916..064a36128 100644
--- a/elephant/spike_train_dissimilarity.py
+++ b/elephant/spike_train_dissimilarity.py
@@ -21,7 +21,7 @@
 """
 
 from __future__ import division, print_function, unicode_literals
-
+import warnings
 import numpy as np
 import quantities as pq
 from neo.core import SpikeTrain
@@ -363,6 +363,18 @@ def van_rossum_distance(spiketrains, time_constant=1.0 * pq.s, sort=True):
     for i, j in np.ndindex(k_dist.shape):
         vr_dist[i, j] = (
             k_dist[i, i] + k_dist[j, j] - k_dist[i, j] - k_dist[j, i])
+
+    # Clip small negative values
+    if np.any(vr_dist < 0):
+        warnings.warn(
+            "van_rossum_distance: very small negative values encountered; "
+            "setting them to zero. Potentially due to floating point error, "
+            "which can occur if spike times are represented as small floating "
+            "point values (e.g., in seconds). A possible way to prevent this "
+            "warning is to use a time unit with better numerical precision, "
+            "e.g., from seconds to milliseconds.", RuntimeWarning)
+        vr_dist = np.maximum(vr_dist, 0.0)
+
     return np.sqrt(vr_dist)
 
 
diff --git a/elephant/test/test_spike_train_dissimilarity.py b/elephant/test/test_spike_train_dissimilarity.py
index 4619d4bba..c856ad878 100644
--- a/elephant/test/test_spike_train_dissimilarity.py
+++ b/elephant/test/test_spike_train_dissimilarity.py
@@ -14,7 +14,7 @@
 import elephant.kernels as kernels
 from elephant.spike_train_generation import StationaryPoissonProcess
 import elephant.spike_train_dissimilarity as stds
-
+import warnings
 from elephant.datasets import download_datasets
 
 
@@ -73,7 +73,6 @@ def setUp(self):
         self.tau7 = 0.01 * s
         self.q7 = 1.0 / self.tau7
         self.t = np.linspace(0, 200, 20000001) * ms
-
     def test_wrong_input(self):
         self.assertRaises(TypeError, stds.victor_purpura_distance,
                           [self.array1, self.array2], self.q3)
@@ -600,6 +599,27 @@ def test_van_rossum_distance(self):
             [self.st21], self.tau3)[0, 0], 0)
         self.assertEqual(len(stds.van_rossum_distance([], self.tau3)), 0)
 
+    def test_van_rossum_distance_regression_small_negative_values(self):
+        """
+        Regression test for issue #679
+        Very small negative value in van_rossum_distance function.
+        Occurs due to floating point precision when
+        spike times are represented as small values
+        These values should be clipped to zero to avoid nans.
+        """
+
+        st24 = SpikeTrain([0.1782, 0.2286, 0.2804, 0.4972, 0.5504],
+                          units='s', t_stop=4.0)
+        tau8 = 0.1 * s
+        # Check small negative values edge case
+        with warnings.catch_warnings(record=True) as w:
+            warnings.simplefilter("always")
+            result = stds.van_rossum_distance([st24, st24], tau8)
+            self.assertTrue(any("very small negative values encountered"
+                            in str(warn.message) for warn in w))
+        self.assertEqual(result[0, 1], 0.0)
+        self.assertFalse(np.any(np.isnan(result)))
+
 
 if __name__ == '__main__':
     unittest.main()