The propagation of large-amplitude hydromagnetic waves of a collisionless anisotropic plasma is treated by using the Chew-Goldberger-Low equations. The generalization of the usual theory of characteristics as applied to this treatment has been developed. It is shown that in such a plasma there are six different types of waves. They incorporate all modes considered in a small-amplitude theory. For a special case of a magnetic field almost parallel to the direction of propagation a fast magnetosonic wave has small density variations proportional to the variations of the square of a magnetic field intensity. A wave equation similar to one used in an isotropic plasma describes the behavior of nonplanar Alfv¿n waves. The simple relation obtained for the averaged large-amplitude perturbations in the transverse Alfv¿n wave is identical to the equation derived on the basis of the WKB approximation.