  We study the symmetry reduction of nonlinear evolution and wave type
differential equations by using operators of non-point symmetry. In our
approach we use both operators of classical and conditional symmetry. It
appears that the combination of non-point and conditional symmetry enables us
to construct not only solutions but B\"acklund transformations too for the
equation under study. We show that the method can be applied to nonevolutionary
partial differential equations.
