In order to elucidate the role of surfaces at nonequilibrium phase transitions, we consider kinetic Ising models with surfaces subjected to a periodic oscillating magnetic field. Whereas, the corresponding bulk system undergoes a continuous nonequilibrium phase transition characterized by the exponents of the equilibrium Ising model, we find that the nonequilibrium surface exponents do not coincide with those of the equilibrium critical surface. In addition, in three space dimensions, the surface phase diagram of the nonequilibrium system differs markedly from that of the equilibrium system.