"Traveling wave"--type solutions of some models with cross-diffusion were considered. It was shown that "cross-diffusion" terms, as opposed to "diffusion" terms, do not increase the dimensionality of the automodel system. The bifurcation approach was used to study the dependence of the wave solutions on the parameters of the models being considered, and the waves were classified. It was shown that, at the same parameter values, both "fast" and "slow" waves can exist and that these waves are described by different automodel systems.