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The velocities of relativistic hydromagnetic waves in a compressible, perfect fluid of infinite conductivity are calculated in the framework of general relativity. In the absence of viscuous and Joule heat losses, the flow is isentropic, and, therefore, the wave surfaces are propagated without change of shape. The velocities are first obtained in terms of the four‐vector magnetic field and then in terms of the three‐dimensional field. Several limiting cases are considered, and, in particular, it is shown under what conditions the expressions reduce to the nonrelativistic forms. Finally, the group velocities are calculated. The existence of a group velocity for such waves is based on the fact that the velocities exhibit a directional dependence. The group velocity in this case is of significance because it is the velocity of energy propagation, just as in the case when dispersion exists.