diff --git a/holoviews/core/spaces.py b/holoviews/core/spaces.py
index 33e9b0cb52..fdacae92fb 100644
--- a/holoviews/core/spaces.py
+++ b/holoviews/core/spaces.py
@@ -817,6 +817,22 @@ def _cache(self, key, val):
         self.data[key] = val
 
 
+    def map(self, map_fn, specs=None, clone=True):
+        """
+        Recursively replaces elements using a map function when the
+        specification applies. Extends regular map with functionality
+        to dynamically apply functions.
+        """
+        deep_mapped = super(DynamicMap, self).map(map_fn, specs, clone)
+        if isinstance(deep_mapped, type(self)):
+            from ..util import Dynamic
+            def apply_map(obj):
+                return obj.map(map_fn, specs, clone)
+            dmap = Dynamic(deep_mapped, shared_data=True, operation=apply_map)
+            return dmap
+        return deep_mapped
+
+
     def relabel(self, label=None, group=None, depth=1):
         """
         Assign a new label and/or group to an existing LabelledData
diff --git a/tests/testdynamic.py b/tests/testdynamic.py
index 13c200a872..93998b2d47 100644
--- a/tests/testdynamic.py
+++ b/tests/testdynamic.py
@@ -1,7 +1,7 @@
 from collections import deque
 
 import numpy as np
-from holoviews import Dimension, NdLayout, GridSpace
+from holoviews import Dimension, NdLayout, GridSpace, Layout
 from holoviews.core.spaces import DynamicMap, HoloMap, Callable
 from holoviews.element import Image, Scatter, Curve, Text
 from holoviews.streams import PositionXY, PositionX, PositionY
@@ -85,6 +85,30 @@ def test_deep_select_slice_kdim_no_match(self):
         dmap = DynamicMap(fn, kdims=[Dimension('Test', range=(10, 20))])
         self.assertEqual(dmap.select(DynamicMap, x=(5, 10))[10], fn(10))
 
+    def test_deep_map_apply_element_function(self):
+        fn = lambda i: Curve(np.arange(i))
+        dmap = DynamicMap(fn, kdims=[Dimension('Test', range=(10, 20))])
+        mapped = dmap.map(lambda x: x.clone(x.data*2), Curve)
+        curve = fn(10)
+        self.assertEqual(mapped[10], curve.clone(curve.data*2))
+
+    def test_deep_map_apply_dmap_function(self):
+        fn = lambda i: Curve(np.arange(i))
+        dmap1 = DynamicMap(fn, kdims=[Dimension('Test', range=(10, 20))])
+        dmap2 = DynamicMap(fn, kdims=[Dimension('Test', range=(10, 20))])
+        mapped = (dmap1 + dmap2).map(lambda x: x[10], DynamicMap)
+        self.assertEqual(mapped, Layout([('DynamicMap.I', fn(10)),
+                                         ('DynamicMap.II', fn(10))]))
+
+    def test_deep_map_apply_dmap_function_no_clone(self):
+        fn = lambda i: Curve(np.arange(i))
+        dmap1 = DynamicMap(fn, kdims=[Dimension('Test', range=(10, 20))])
+        dmap2 = DynamicMap(fn, kdims=[Dimension('Test', range=(10, 20))])
+        layout = (dmap1 + dmap2)
+        mapped = layout.map(lambda x: x[10], DynamicMap, clone=False)
+        self.assertIs(mapped, layout)
+
+
 
 class DynamicTestCallableBounded(ComparisonTestCase):