The nonequilibrium or dynamic phase transitions are studied, within a mean-field approach, in the kinetic Ising model on a two-layer square lattice consisting of spin-1/2 ions in the presence of a time varying (sinusoidal) magnetic field has been studied by using Glauber-type stochastic dynamics. The dynamic equations of motion are obtained in terms of the intralayer coupling constants J(1) and J(2) for the first and second layer, respectively, and interlayer coupling constant J(3) between these two layers. The nature (first- or second-order) of the transitions is characterized by investigating the behavior of the thermal variations of the dynamic order parameters. The dynamic phase transitions are obtained and the dynamic phase diagrams are constructed in the plane of the reduced temperature versus the amplitude of the magnetic field and found fourteen fundamental types of phase diagrams. Phase diagrams exhibit one, two or three dynamic tricritical points for various values of J(2)/vertical bar J(1)vertical bar and J(3)/vertical bar J(1)vertical bar. Besides the paramagnetic (p), ferromagnetic (0 and compensated (c) phases, there were the f + c, f + sf, c + sf, af + p, m + p, f + m and c + af, where the af, sf and m are the anti ferromagnetic, surface ferromagnetic and mixed phases respectively. Coexistence phase regions also exist in the system. (C) 2008 Elsevier B.V. All rights reserved.