Two-quantum microwave magnetic resonance transitions corresponding to ∆MJ=+/-2 have been observed for both stable isotopes of atomic chlorine, Cl35 and Cl37. The experimentally observed and theoretically predicted positions of the two-quantum transitions agree within 13 parts per million, which was the precision of the experiment. The power dependence of the two-quantum transitions has been measured and checked with a "variation of constants" treatment of the microwave-induced probability amplitudes, and agreement has been found. Variations in intensity between corresponding ∆MJ=+/-1 and ∆MJ=+/-2 resonances were observed and analyzed on the basis of time-dependent perturbation theory and the Schwinger-Karplus expression for the line shape of a collision-broadened resonance with saturation. Satisfactory agreement with theory is found for these intensity variations. The linewidths for the ∆MJ=+/-2 lines are approximately half of that for the ∆MJ=+/-1 lines; this is in agreement with the results of time-dependent perturbation theory.