The main features of wave propagation in gyrotropic media are compared with wave propagation in anisotropic media. The results of numerical modelling are presented for three typical seismic exploration models. The first two models are azimuthally anisotropic media (of orthorombic symmetry system, group 2m) without and with gyration. The third model is a gyrotropic transversely isotropic medium with a vertical symmetry axis. The computations have been made for propagation of shear waves along the Vertical symmetry axis. For sufficiently short wave paths (in our models less than 400 m) the two-component (x, y) seismograms are similar for all three models. For longer paths both signal shape and signal duration for the first and the third model differ noticeably. Some evidence (experimental data and a micromodel) is given to show that the gyrotropy of rocks does exist or, at least, can exist.