The trigger mechanism in active object-oriented database systems is known to be a good tool for describing user-defined integrity constraints. It cannot adequately support, however, certain integrity constrains specified on the objects in class composition hierarchy. Those are the cases where the constraints must be maintained in the forward direction along the composition hierarchy as well as in the backward direction We call theses kinds of problems "backward propagation problem" and investigate several ways to resolve them using the currently available techniques. Based on them, a new constructor, called CONSTRAIN $T^{cch}$, is proposed. The constructor can be realized with enhanced facilities for active OODBMS which we recommend in this paper.d facilities for active OODBMS which we recommend in this paper.r.