diff --git a/Hash_map/include/CGAL/Tools/chained_map.h b/Hash_map/include/CGAL/Tools/chained_map.h
index 351a239f44a..042065b77db 100644
--- a/Hash_map/include/CGAL/Tools/chained_map.h
+++ b/Hash_map/include/CGAL/Tools/chained_map.h
@@ -76,11 +76,10 @@ private:
 public:
    static constexpr std::size_t min_size = 32;
    static constexpr std::size_t default_size = 512;
-   typedef chained_map_elem<T>*  chained_map_item;
-   typedef chained_map_item item;
+   typedef chained_map_elem<T>*  Item;
 
-   std::size_t index(chained_map_item it) const { return it->k; }
-   T&            inf(chained_map_item it) const { return it->i; }
+   std::size_t index(Item it) const { return it->k; }
+   T&            inf(Item it) const { return it->i; }
 
    chained_map(std::size_t n = default_size, const T& d = T());
    chained_map(const chained_map<T, Allocator>& D);
@@ -92,14 +91,14 @@ public:
    {
      if(!table)
        return;
-     for (chained_map_item item = table ; item != table_end ; ++item)
+     for (Item item = table ; item != table_end ; ++item)
        destroy(item);
      alloc.deallocate(table, table_end - table);
    }
 
-   T& access(chained_map_item p, std::size_t x);
+   T& access(Item p, std::size_t x);
    T& access(std::size_t x);
-   chained_map_item lookup(std::size_t x) const;
+   Item lookup(std::size_t x) const;
    void statistics() const;
 };
 
@@ -109,7 +108,7 @@ inline T& chained_map<T, Allocator>::access(std::size_t x)
   if(!table)
     init_table(reserved_size);
 
-  chained_map_item p = HASH(x);
+  Item p = HASH(x);
 
   if ( p->k == x ) {
      return p->i;
@@ -140,7 +139,7 @@ void chained_map<T, Allocator>::init_table(std::size_t n)
   free = table + t;
   table_end = table + t + t/2;
 
-  for (chained_map_item p = table; p < free; p++)
+  for (Item p = table; p < free; p++)
   { p->succ = nullptr;
     p->k = nullptrKEY;
   }
@@ -149,7 +148,7 @@ void chained_map<T, Allocator>::init_table(std::size_t n)
 
 template <typename T, typename Allocator>
 inline void chained_map<T, Allocator>::insert(std::size_t x, T y)
-{ chained_map_item q = HASH(x);
+{ Item q = HASH(x);
   if ( q->k == nullptrKEY ) {
     q->k = x;
     q->i = y;
@@ -169,16 +168,16 @@ void chained_map<T, Allocator>::rehash()
   chained_map_elem<T>* old_table_end = table_end;
   chained_map_elem<T>* old_free = free;
 
-  chained_map_item old_table_mid = table + table_size;
+  Item old_table_mid = table + table_size;
 
   init_table(2*table_size);
 
-  chained_map_item p;
+  Item p;
 
   for(p = old_table; p < old_table_mid; p++)
   { std::size_t x = p->k;
     if ( x != nullptrKEY ) // list p is non-empty
-    { chained_map_item q = HASH(x);
+    { Item q = HASH(x);
       q->k = x;
       q->i = p->i;
     }
@@ -190,16 +189,16 @@ void chained_map<T, Allocator>::rehash()
     p++;
   }
 
-  for (chained_map_item item = old_table ; item != old_table_end ; ++item)
+  for (Item item = old_table ; item != old_table_end ; ++item)
     destroy(item);
   alloc.deallocate(old_table, old_table_end - old_table);
 }
 
 
 template <typename T, typename Allocator>
-T& chained_map<T, Allocator>::access(chained_map_item p, std::size_t x)
+T& chained_map<T, Allocator>::access(Item p, std::size_t x)
 {
-  chained_map_item q = p->succ;
+  Item q = p->succ;
   while (q && q->k != x) q = q->succ;
   if (q)
   {
@@ -240,7 +239,7 @@ chained_map<T, Allocator>::chained_map(const chained_map<T, Allocator>& D)
 {
   init_table(D.table_size);
 
-  for(chained_map_item p = D.table; p < D.free; p++)
+  for(Item p = D.table; p < D.free; p++)
   { if (p->k != nullptrKEY || p >= D.table + D.table_size)
     { insert(p->k,p->i);
       //D.copy_inf(p->i);  // see chapter Implementation
@@ -255,7 +254,7 @@ chained_map<T, Allocator>& chained_map<T, Allocator>::operator=(const chained_ma
 
   init_table(D.table_size);
 
-  for(chained_map_item p = D.table; p < D.free; p++)
+  for(Item p = D.table; p < D.free; p++)
   { if (p->k != nullptrKEY || p >= D.table + D.table_size)
     { insert(p->k,p->i);
       //copy_inf(p->i);    // see chapter Implementation
@@ -277,7 +276,7 @@ void chained_map<T, Allocator>::clear()
   if(!table)
     return;
 
-  for (chained_map_item item = table ; item != table_end ; ++item)
+  for (Item item = table ; item != table_end ; ++item)
     destroy(item);
   alloc.deallocate(table, table_end - table);
 
@@ -285,13 +284,13 @@ void chained_map<T, Allocator>::clear()
 }
 
 template <typename T, typename Allocator>
-typename chained_map<T, Allocator>::chained_map_item
+typename chained_map<T, Allocator>::Item
 chained_map<T, Allocator>::lookup(std::size_t x) const
 {
   if(!table)
     return nullptr;
 
-  chained_map_item p = HASH(x);
+  Item p = HASH(x);
   while (p && p->k != x)
   { p = p->succ; }
   return p;
@@ -301,7 +300,7 @@ template <typename T, typename Allocator>
 void chained_map<T, Allocator>::statistics() const
 { std::cout << "table_size: " << table_size <<"\n";
   std::size_t n = 0;
-  for (chained_map_item p = table; p < table + table_size; p++)
+  for (Item p = table; p < table + table_size; p++)
      if (p ->k != nullptrKEY) n++;
   std::size_t used_in_overflow = free - (table + table_size );
   n += used_in_overflow;
diff --git a/Hash_map/include/CGAL/Unique_hash_map.h b/Hash_map/include/CGAL/Unique_hash_map.h
index 58e830a34c1..09d3dc9610c 100644
--- a/Hash_map/include/CGAL/Unique_hash_map.h
+++ b/Hash_map/include/CGAL/Unique_hash_map.h
@@ -47,7 +47,7 @@ public:
 
 private:
     typedef internal::chained_map<Data, Allocator>   Map;
-    typedef typename Map::item                       Item;
+    typedef typename Map::Item                       Item;
 
 private:
     Hash_function  m_hash_function;