We calculate semianalytically the spin-wave eigenmodes and frequencies of an infinite thin film with periodically modulated exchange bias field. We show that both localized and propagating modes exist in this system and that band gaps exist at the edges of the Brillouin zone. The spin-wave frequencies and band gaps can be tailored by changing the period of the superlattice. This method is of technological relevance as the modification of the spin-wave spectrum can be achieved without any change in topography. (c) 2006 American Institute of Physics.