We have modeled interacting plane-parallel membranes as viscoelastic multilayered films. A linear dynamic analysis was used. It gave the general conditions for stability of membrane systems having an arbitrary number of membranes and films. The particular cases of one, two and three interacting layers were considered in detail. The results suggest a strong dependence of the stability of membrane systems on the interfacial tensions and the thickness of individual membranes and films and rather weak dependence on their viscosities and elasticities. The theoretical predictions are in semi-quantitative agreement with data on electrically induced membrane fusion in dielectrophoresis.