Following Chu [inNon‐EquilibriumFlows, edited by P. P. Wegener (Dekker, New York, 1970), Vol. II, p. 37], the phenomena associated with the propagation of acceleration waves in nonequilibrium magnetogasdynamic flow, which is induced by the motion of a piston advancing with finite acceleration into a constant state of rest, are studied. Also studied is the characteristic path by using the characteristics of the governing quasilinear system as the reference coordinate system. A differential equation governing the growth and decay of an acceleration wave is derived. The critical time when the breakdown of the characteristic solution occurs in the neighborhood of the leading frozen characteristic is obtained; that is, when all the characteristics will pile up at the wave front to form a shock wave. It is shown that for the slow relaxation process the effect of the magnetic field is to slow down the motion of the breakdown point along the leading frozen characteristic, and thus to increase the cylindrical shock formation time. However, the effect of the magnetic field on expansion waves is to enhance the decay rate. For the quick relaxation process, however, the effect of the magnetic field on compressive waves is to cause an early shock formation, while the effect on expansion waves is to decrease the decay rate.