A theory is developed for dispersion characteristics of spin waves in ferromagnetic films taking into account both dipole-dipole and exchange interactions, crystallographic anisotropy and mixed exchange boundary conditions on the film surfaces. An arbitrary orientation of the external bias magnetic field with respect to the orientation of crystallographic axes and the film normal is assumed. The influence of crystallographic anisotropy on the spin wave spectrum of a ferromagnetic film is discussed. The theoretical results obtained are compared with the results of experiments performed in yttrium-iron garnet (YIG) and Mn-ferrospinel films.