Results of investigating nonlinear regimes of the homogeneous precessional dynamics of magnetization in iron – garnet films with various orientations of crystallographic axes and in metallic thin-film structures are presented. Attention is primarily focused on static and dynamic bistabilities, which, under the effect of an ac magnetic field, lead to the magnetization reversal of the systems, bifurcational changes in the magnetization precession amplitude, or the establishment of both stochastic and complex regular (including auto-oscillating) precessional regimes. The bifurcation diagrams considered reveal diverse possibilities of efficiently controlling the nonlinear dynamics of magnetization in thin-film structures by varying external magnetic fields.