Nonlinear optics of magnetic crystals is a very recent field that exhibits a number of unusual optical phenomena. Using the electric dipole approximation we discuss the crystallographic and magnetization-induced nonlinear susceptibilities that coexist in magnetic crystals. It is the interference between the nonlinear optical waves of different origin that is the source of novel magneto-optical effects, such as transversal linear in M effect at normal incidence, circular magnetic dichroism with no equivalence between light helicity and magnetization direction change, etc., that have no equivalent in linear optics. As a model system for experimental studies we used thin epitaxial films of magnetic garnets grown on substrates with different crystallographic orientations. The second harmonic generation (SHG) was studied in the spectral range of 0.71-0.84 μm. These experiments were done in both transverse and longitudinal geometries. The experimental data on the SHG rotational anisotropy perfectly confirm the predicted effects.