  The quantization procedure for both N=1 and N=2 supersymmetric Korteweg-de
Vries (SUSY KdV) hierarchies is constructed. Namely, the quantum counterparts
of the monodromy matrices, built by means of the integrated vertex operators,
are shown to satisfy a specialization of reflection equation, leading to the
quantum integrable theory. The relation of such models to the study of
integrable perturbed superconformal and topological models is discussed.
