In R. L. Wilder's book [2] the open and closed generalized manifolds are extensively studied. However, no study is made of the generalized manifold with boundary nor is a definition of such a space given except in the case of the generalized closed n-cell. A definition of a generalized manifold with boundary was given by the author in his paper [1]. Before undertaking the study of further properties of these manifolds it seems appropriate to characterize the manifolds with boundary in terms of the open and closed manifolds of Wilder. It is to that purpose that this paper is directed and in particular the generalized closed n-cell of Wilder is characterized as a special manifold with boundary.