Magnetoresistance measurements performed at 4.2 K up to B = 22 T applied along the tetragonal c-axis on antiferromagnetic single crystalline Ce(Rh_1-xRu_x)₂Si₂ solid solutions (x = 0.05, 0.1 and 0.2) are reported. The 4.2 K resistivity, i.e. the residual resistivity, \rho ₀, is strongly reduced in 22 T, showing that the large increase of \rho ₀ with x can not be attributed to disorder alone. The results evidence two transitions at fields B_{c}1 and B_{c}2 which correspond to metamagnetic transitions, similar to the two step transition occuring in CeRh₂Si₂ at 25.8 and 26.3 T, respectively. B_{c}1 and B_{c}2 decrease rapidly with increasing x, and their splitting increases (showing some analogy with measurements reported for Ge doped CeRh₂Si₂). These variations and the rapid decrease of T_{N}1 (which has vanished for x = 0.35), are discussed.

PACS numbers: 71.27.+a, 74.25.Fy, 74.25.Ha, 75.30.Kz