diff --git a/libgomp/libgomp.h b/libgomp/libgomp.h
index f98cccd8b66..089393846d1 100644
--- a/libgomp/libgomp.h
+++ b/libgomp/libgomp.h
@@ -1163,6 +1163,8 @@ struct target_mem_desc;
 /* Special value for refcount - tgt_offset contains target address of the
    artificial pointer to "omp declare target link" object.  */
 #define REFCOUNT_LINK     (REFCOUNT_SPECIAL | 1)
+/* Special value for refcount - created through acc_map_data.  */
+#define REFCOUNT_ACC_MAP_DATA (REFCOUNT_SPECIAL | 2)
 
 /* Special value for refcount - structure element sibling list items.
    All such key refounts have REFCOUNT_STRUCTELEM bits set, with _FLAG_FIRST
diff --git a/libgomp/oacc-mem.c b/libgomp/oacc-mem.c
index ba48a1ccbb7..d590806b5cd 100644
--- a/libgomp/oacc-mem.c
+++ b/libgomp/oacc-mem.c
@@ -411,7 +411,8 @@ acc_map_data (void *h, void *d, size_t s)
       assert (n->refcount == 1);
       assert (n->dynamic_refcount == 0);
       /* Special reference counting behavior.  */
-      n->refcount = REFCOUNT_INFINITY;
+      n->refcount = REFCOUNT_ACC_MAP_DATA;
+      n->dynamic_refcount = 1;
 
       if (profiling_p)
 	{
@@ -455,12 +456,7 @@ acc_unmap_data (void *h)
       gomp_fatal ("[%p,%d] surrounds %p",
 		  (void *) n->host_start, (int) host_size, (void *) h);
     }
-  /* TODO This currently doesn't catch 'REFCOUNT_INFINITY' usage different from
-     'acc_map_data'.  Maybe 'dynamic_refcount' can be used for disambiguating
-     the different 'REFCOUNT_INFINITY' cases, or simply separate
-     'REFCOUNT_INFINITY' values per different usage ('REFCOUNT_ACC_MAP_DATA'
-     etc.)?  */
-  else if (n->refcount != REFCOUNT_INFINITY)
+  else if (n->refcount != REFCOUNT_ACC_MAP_DATA)
     {
       gomp_mutex_unlock (&acc_dev->lock);
       gomp_fatal ("refusing to unmap block [%p,+%d] that has not been mapped"
@@ -468,13 +464,12 @@ acc_unmap_data (void *h)
 		  (void *) h, (int) host_size);
     }
 
-  struct target_mem_desc *tgt = n->tgt;
+  /* This should hold for all mappings created by acc_map_data. We are however
+     removing this mapping in a "finalize" manner, so dynamic_refcount > 1 does
+     not matter.  */
+  assert (n->dynamic_refcount >= 1);
 
-  if (tgt->refcount == REFCOUNT_INFINITY)
-    {
-      gomp_mutex_unlock (&acc_dev->lock);
-      gomp_fatal ("cannot unmap target block");
-    }
+  struct target_mem_desc *tgt = n->tgt;
 
   /* Above, we've verified that the mapping must have been set up by
      'acc_map_data'.  */
@@ -519,7 +514,8 @@ goacc_map_var_existing (struct gomp_device_descr *acc_dev, void *hostaddr,
     }
 
   assert (n->refcount != REFCOUNT_LINK);
-  if (n->refcount != REFCOUNT_INFINITY)
+  if (n->refcount != REFCOUNT_INFINITY
+      && n->refcount != REFCOUNT_ACC_MAP_DATA)
     n->refcount++;
   n->dynamic_refcount++;
 
@@ -683,13 +679,30 @@ goacc_exit_datum_1 (struct gomp_device_descr *acc_dev, void *h, size_t s,
 
   assert (n->refcount != REFCOUNT_LINK);
   if (n->refcount != REFCOUNT_INFINITY
+      && n->refcount != REFCOUNT_ACC_MAP_DATA
       && n->refcount < n->dynamic_refcount)
     {
       gomp_mutex_unlock (&acc_dev->lock);
       gomp_fatal ("Dynamic reference counting assert fail\n");
     }
 
-  if (finalize)
+  if (n->refcount == REFCOUNT_ACC_MAP_DATA)
+    {
+      if (finalize)
+	{
+	  /* Mappings created by acc_map_data are returned to initial
+	     dynamic_refcount of 1. Can only be deleted by acc_unmap_data.  */
+	  n->dynamic_refcount = 1;
+	}
+      else if (n->dynamic_refcount)
+	{
+	  /* When mapping is created by acc_map_data, dynamic_refcount must be
+	     maintained at >= 1.  */
+	  if (n->dynamic_refcount > 1)
+	    n->dynamic_refcount--;
+	}
+    }
+  else if (finalize)
     {
       if (n->refcount != REFCOUNT_INFINITY)
 	n->refcount -= n->dynamic_refcount;
@@ -1131,7 +1144,8 @@ goacc_enter_data_internal (struct gomp_device_descr *acc_dev, size_t mapnum,
 	    }
 	  /* This is a special case because we must increment the refcount by
 	     the number of mapped struct elements, rather than by one.  */
-	  if (n->refcount != REFCOUNT_INFINITY)
+	  if (n->refcount != REFCOUNT_INFINITY
+	      && n->refcount != REFCOUNT_ACC_MAP_DATA)
 	    n->refcount += groupnum - 1;
 	  n->dynamic_refcount += groupnum - 1;
 	}
@@ -1203,7 +1217,8 @@ goacc_enter_data_internal (struct gomp_device_descr *acc_dev, size_t mapnum,
 	      processed = true;
 	    }
 	  else
-	    assert (n->refcount != REFCOUNT_INFINITY);
+	    assert (n->refcount != REFCOUNT_INFINITY
+		    && n->refcount != REFCOUNT_ACC_MAP_DATA);
 
 	  for (size_t j = 0; j < tgt->list_count; j++)
 	    if (tgt->list[j].key == n)
diff --git a/libgomp/target.c b/libgomp/target.c
index bcc86051601..c9dcb8761e5 100644
--- a/libgomp/target.c
+++ b/libgomp/target.c
@@ -481,7 +481,9 @@ gomp_increment_refcount (splay_tree_key k, htab_t *refcount_set)
 
   uintptr_t *refcount_ptr = &k->refcount;
 
-  if (REFCOUNT_STRUCTELEM_FIRST_P (k->refcount))
+  if (k->refcount == REFCOUNT_ACC_MAP_DATA)
+    refcount_ptr = &k->dynamic_refcount;
+  else if (REFCOUNT_STRUCTELEM_FIRST_P (k->refcount))
     refcount_ptr = &k->structelem_refcount;
   else if (REFCOUNT_STRUCTELEM_P (k->refcount))
     refcount_ptr = k->structelem_refcount_ptr;
@@ -528,7 +530,9 @@ gomp_decrement_refcount (splay_tree_key k, htab_t *refcount_set, bool delete_p,
 
   uintptr_t *refcount_ptr = &k->refcount;
 
-  if (REFCOUNT_STRUCTELEM_FIRST_P (k->refcount))
+  if (k->refcount == REFCOUNT_ACC_MAP_DATA)
+    refcount_ptr = &k->dynamic_refcount;
+  else if (REFCOUNT_STRUCTELEM_FIRST_P (k->refcount))
     refcount_ptr = &k->structelem_refcount;
   else if (REFCOUNT_STRUCTELEM_P (k->refcount))
     refcount_ptr = k->structelem_refcount_ptr;
@@ -561,6 +565,10 @@ gomp_decrement_refcount (splay_tree_key k, htab_t *refcount_set, bool delete_p,
   else if (*refcount_ptr > 0)
     *refcount_ptr -= 1;
 
+  /* Force back to 1 if this is an acc_map_data mapping.  */
+  if (k->refcount == REFCOUNT_ACC_MAP_DATA && *refcount_ptr == 0)
+    *refcount_ptr = 1;
+
  end:
   if (*refcount_ptr == 0)
     {
diff --git a/libgomp/testsuite/libgomp.oacc-c-c++-common/lib-96.c b/libgomp/testsuite/libgomp.oacc-c-c++-common/lib-96.c
new file mode 100644
index 00000000000..7bc55b94f33
--- /dev/null
+++ b/libgomp/testsuite/libgomp.oacc-c-c++-common/lib-96.c
@@ -0,0 +1,36 @@
+/* { dg-do run } */
+/* { dg-skip-if "" { *-*-* } { "-DACC_MEM_SHARED=1" } } */
+
+/* Test if acc_unmap_data has implicit finalize semantics.  */
+
+#include <stdlib.h>
+#include <openacc.h>
+
+int
+main (int argc, char **argv)
+{
+  const int N = 256;
+  unsigned char *h;
+  void *d;
+
+  h = (unsigned char *) malloc (N);
+
+  d = acc_malloc (N);
+
+  acc_map_data (h, d, N);
+
+  acc_copyin (h, N);
+  acc_copyin (h, N);
+  acc_copyin (h, N);
+
+  acc_unmap_data (h);
+
+  if (acc_is_present (h, N))
+    abort ();
+
+  acc_free (d);
+
+  free (h);
+
+  return 0;
+}
diff --git a/libgomp/testsuite/libgomp.oacc-c-c++-common/unmap-infinity-1.c b/libgomp/testsuite/libgomp.oacc-c-c++-common/unmap-infinity-1.c
index 872f0c1de5c..9ed9fa7e413 100644
--- a/libgomp/testsuite/libgomp.oacc-c-c++-common/unmap-infinity-1.c
+++ b/libgomp/testsuite/libgomp.oacc-c-c++-common/unmap-infinity-1.c
@@ -10,7 +10,7 @@ main (int argc, char *argv[])
 {
   acc_init (acc_device_default);
   acc_unmap_data ((void *) foo);
-/* { dg-output "libgomp: cannot unmap target block" } */
+/* { dg-output "libgomp: refusing to unmap block \\\[\[0-9a-fA-FxX\]+,\\\+64\\\] that has not been mapped by 'acc_map_data'" } */
   return 0;
 }