[en] The authors study nonstandard shock wave similarity solutions for three multispeed discrete boltzmann models: (1) the square 8υ_i model with speeds 1 and √2 with the x axis along one median, (2) the Cabannes cubic 14υ_i model with speeds 1 and √3 and the x axis perpendicular to one face, and (3) another 14υ_i model with speeds 1 and √2. These models have five independent densities and two nonlinear Riccati-coupled equations. The standard similarity shock waves, solutions of scalar Riccati equations, are monotonic and the same behavior holds for the conservative macroscopic quantities. First, the exact similarity shock-wave solutions of coupled Riccati equations are determined and the nonmonotonic behavior for one density and a smaller effect for one conservative macroscopic quantity are observed when a violation of the microreversibility is allowed. Second, new results are obtained on the Whitham weak shock wave propagation. Third, the corresponding dynamical system is numerically solved, with microreversibility satisfied or not, and the analogous nonmonotonic behavior is observed. 9 refs., 2 figs., 1 tab