diff --git a/Lib/ipaddress.py b/Lib/ipaddress.py
index 7024339..ac1143a 100644
--- a/Lib/ipaddress.py
+++ b/Lib/ipaddress.py
@@ -1509,6 +1509,8 @@
 
         if self._prefixlen == (self._max_prefixlen - 1):
             self.hosts = self.__iter__
+        elif self._prefixlen == (self._max_prefixlen):
+            self.hosts = lambda: [IPv4Address(addr)]
 
     @property
     @functools.lru_cache()
@@ -2212,6 +2214,8 @@
 
         if self._prefixlen == (self._max_prefixlen - 1):
             self.hosts = self.__iter__
+        elif self._prefixlen == self._max_prefixlen:
+            self.hosts = lambda: [IPv6Address(addr)]
 
     def hosts(self):
         """Generate Iterator over usable hosts in a network.
diff --git a/Lib/test/test_ipaddress.py b/Lib/test/test_ipaddress.py
index f4a4afb..bbb3fc8 100644
--- a/Lib/test/test_ipaddress.py
+++ b/Lib/test/test_ipaddress.py
@@ -1424,6 +1424,15 @@
         self.assertEqual(list(ipaddress.ip_network(str_args).hosts()),
                          list(ipaddress.ip_network(tpl_args).hosts()))
 
+        # special case where the network is a /32
+        addrs = [ipaddress.IPv4Address('1.2.3.4')]
+        str_args = '1.2.3.4/32'
+        tpl_args = ('1.2.3.4', 32)
+        self.assertEqual(addrs, list(ipaddress.ip_network(str_args).hosts()))
+        self.assertEqual(addrs, list(ipaddress.ip_network(tpl_args).hosts()))
+        self.assertEqual(list(ipaddress.ip_network(str_args).hosts()),
+                         list(ipaddress.ip_network(tpl_args).hosts()))
+
         addrs = [ipaddress.IPv6Address('2001:658:22a:cafe::'),
                  ipaddress.IPv6Address('2001:658:22a:cafe::1')]
         str_args = '2001:658:22a:cafe::/127'
@@ -1432,10 +1441,10 @@
         self.assertEqual(addrs, list(ipaddress.ip_network(tpl_args).hosts()))
         self.assertEqual(list(ipaddress.ip_network(str_args).hosts()),
                          list(ipaddress.ip_network(tpl_args).hosts()))
-        addrs = [ipaddress.IPv6Address('2001:658:22a:cafe::'),
-                 ipaddress.IPv6Address('2001:658:22a:cafe::1')]
-        str_args = '2001:658:22a:cafe::/127'
-        tpl_args = ('2001:658:22a:cafe::', 127)
+
+        addrs = [ipaddress.IPv6Address('2001:658:22a:cafe::1'), ]
+        str_args = '2001:658:22a:cafe::1/128'
+        tpl_args = ('2001:658:22a:cafe::1', 128)
         self.assertEqual(addrs, list(ipaddress.ip_network(str_args).hosts()))
         self.assertEqual(addrs, list(ipaddress.ip_network(tpl_args).hosts()))
         self.assertEqual(list(ipaddress.ip_network(str_args).hosts()),