Steepening of relativistic magnetohydrodynamic (MHD) small-amplitude waves is discussed with the nonlinear effects taken into account. First, the propagation properties of the slow, intermediate and fast MHD waves are examined, and then, a condition is derived such that the second of two waves of the same mode launched successively, catches up with the first wave. The condition includes a requirement that ∂(2(w/n2)/∂p2>0, indicating a positive pressure variation of the relativistic compressibility, wherewis the heat function,nis the particle number density andpis the pressure. The same condition is also obtained using the theory of relativistic MHDsimplewaves. Thus, although the intermediate MHD wave does not steepen, the slow and fast MHD waves can steepen owing to the nonlinear effects, producing infinitely large gradients and eventually dissipating after formation of a shock. However, in the extreme-relativistic limit, in which the magnetic energy is much larger than the rest mass plus thermal energy, the steepening rate tends to zero, consistent with relativity.