The "liquid film motor," a novel device with important implications for basic research and technology, is analyzed. It works perfectly with both direct current (dc) and alternating current (ac) fields. We develop a mathematical model describing electrohydrodynamical (EHD) motions induced by ac fields, which are more complex and have wider technological applications than those produced by dc fields. The main characteristics of these motions, derived in our paper and in full agreement with the experimental ones, are as follows: (i) Rotation of the film requires that the frequencies of the ac fields are exactly the same and their magnitudes surpass a threshold, which depends on their phase difference. (ii) Vibrations may be induced by fields with different frequencies. (iii) The EHD motions strongly depend on the polarization induced by the external electric field. However, these motions are little affected by the liquid's electrical conductivity, viscosity, dielectric constant, and density. Our model also predicts several features, which have yet to be experimentally verified.