Subharmonic microwave-induced Josephson step structure is often observed in superconducting junctions that exhibit subharmonic gap structure. The two theories, multiparticle tunneling and self-coupling due to an electromagnetic field set up by the ac Josephson current, which have been suggested to explain the subharmonic gap structure are investigated with respect to the possible existence of subharmonic Josephson steps. Also treated is a Ginzburg-Landau calculation of the current-phase relation for Josephson junctions. All three theories give subharmonic Josephson steps with the same microwave-power dependence. The temperature dependence of the subharmonic step structure and the subharmonic gap structure is discussed. It seems the self-coupling is the main cause for both effects in tunnel junctions and for the subharmonic gap structure in Dayem bridges, while the subharmonic step structure in the Dayem bridge seems to be a geometrical effect related to “multiparticle” transfer processes.