Experiments on both point-contact junctions (Nb-Nb) and on small area thin-film tunnel junctions (Sn-O-Sn) show that applied 4-mm radiation produces satellites associated with "subharmonic" gap structure as well as the familiar microwave-assisted tunneling structure associated with the superconducting energy gap itself. The location in voltage of all these structures is given by eV=(2Δ±nh ν) / m, where 2Δ is the superconducting energy gap, ν is the applied frequency, h is Planck's constant, e is the magnitude of the electronic charge, V is the dc voltage drop across the junction, and m and n are integers: m=1,2,3,… and n=0,1,2,…. The power dependence of the satellite structure and the microwave-assisted tunneling structure is consistent for all junctions tested with the expression Jn2(m e Vrf / h ν), where Jn(x) is the ordinary Bessel function of order n, Vrf is the amplitude of the induced microwave voltage drop accross the junction, and the other quantities are as defined above. A distinction between the explanations—multiparticle tunneling and nonlinear self-coupling—of the subharmonic gap structure cannot, however, be made on the basis of the observed power dependence. Hence other properties such as relative amplitude and line shape are considered and it is concluded that self-coupling mechanisms seem able to account for all the observations, whereas multiparticle tunneling may be discarded as the sole explanation of the structure.