Top-context-free tree languages (called cor gulier by Arnold and Dauchet 1, 2]) constitute a natural subclass of context-free tree languages. In this paper, we give further evidence for the importance of this class by exhibiting certain closure properties. We systematically treat closure under the operations replacementand substitutionas well as under the corresponding iteration operations. Several other well-known language classes are considered as well. Furthermore, various characterizations of the regular top-context-free languages are given, among others by means of restricted regular expressions.