  The functional relations of the transfer matrices of fusion hierachies for
six- and eight-vertex models with open boundary conditions have been presented
in this paper. We have shown the su($2$) fusion rule for the models with more
general reflection boundary conditions, which are represented by off-diagonal
reflection matrices. Also we have discussed some physics properties which are
determined by the functional relations. Finally the intertwining relation
between the reflection $K$ matrices for the vertex and SOS models is discussed.
