We report an experimental investigation of Shockley-Read and Auger lifetimes in InAs-Ga1-xInxSb and InAs-GaSb superlattices, based on measurements of the photoconductive response to excitation by a frequency-doubled CO2 laser (4.63 mum) at intensities up to 100 kW/cm2. Results at 77 K for low excitation levels yield Shockley-Read lifetimes between 0.13 and 6 ns. The scaling of the lifetime with carrier concentration also provides the first determinations of Auger coefficients in narrow-gap type II superlattices : gamma3 almost-equal-to 8 X 10(-25) cm6/s at 300 K and gamma3 almost-equal-to 1.3 x 10(-27) cm6/s at 77 K. The observed Auger lifetime at 77 K is two orders of magnitude longer than that in Hg1-xCdxTe with the same energy gap, which has highly favorable implications for InAs-Ga1-xInxSb superlattices in both IR detector and nonlinear optical applications.