In recent years there has been much interest in the physics and possible technological applications of liquid crystal-based tuneable Bragg gratings. Such optical devices can be realised using special composite materials based on a sequence of polymeric sheets alternated by layers containing only liquid crystal, sometimes known as Policryps and Poliphem. Recent experiments have clearly demonstrated a peculiar dependence of relaxation times on actual external field applied (both amplitude and duration) after switching off the operating voltage. We propose a theoretical model of director reorientation in such composites, in which both bulk behaviour in the LC stripes and interfacial polymer-LC interaction is taken into account. Within this model we explain the dynamical behaviour of holographic gratings characterized by a nematic film-polymer slice sequence structure, as well as other polymer-LC phase separated composites.