We have studied GaxIn1−xAsySb1−y/GaSb heterostructures for x=0.84 and y=0.14 using the photoacoustic technique with the heat transmission configuration. A theoretical model, which includes all the possible nonradiative recombination mechanisms that contribute to heat generation, was developed to calculate the photoacoustic signal for this type of heterostructure. The Auger recombination lifetime τAuger was determined by fitting our experimental results to the calculated frequency dependence of the theoretical photoacoustic signal. The obtained value for τAuger is compatible with those reported in the literature for semiconductors with band-gap energies below and above 0.5 eV, the energy region where there is a lack of experimental τAuger values.