On large deflections of viscoelastic plates1This work was supported by Grant 1/5094/1998 of the Grant Agency of the Slovak Republic.1

We shall deal with the system of von Kármán equations describing great deflections of thin plates. Most papers mainly from the 1960s and the 1970s are devoted to stationary nonlinear systems with elliptic main parts. We shall concentrate on viscoelastic plates modelled by a nonstationary pseudo-parabolic system in the case of short memory and by a system with a memory term in the long memory case. The Rothe's method converts the nonstationary problems to the sequence of stationary von Kármán equations approximating weak solutions of the original problems.