Passive Q-switching of a 1.34 µm Nd3+:YAlO3 laser and a 1.54 µm Er3+:glass laser using Co2+:MgAl2O4(Co2+:MALO) and Co2+:LaMgAl11O19(Co2+:LMA) crystals as saturable absorbers are demonstrated. Q-switched laser pulses of 110 ns (75 ns) in duration and up to 10 mJ (3.8 mJ) energy at 1.34 µm and 56 ns (40 ns) in duration and up to 2.7 mJ (4.5 mJ) in energy at 1.54 µm were obtainable for the Co2+:MALO(Co2+:LMA) crystals. Using the Co2+:MALO as saturable absorber, mode-locked 1.34 µm Nd3+:YAlO3 laser single pulses were obtained to be ~300 ps duration and up to 0.2 mJ energy. Differential absorption spectra recorded with picosecond pump-probe technique and absorption saturation of the Co2+:MALO and Co2+:LMA crystals are investigated.