We have measured the saturation of optical absorption in GaSb at wavelengths close to the band gap, and have determined the nonlinear absorption (α2) and refraction (n2) coefficients. At liquid-helium temperature a sharp free-exciton absorption line is observed which saturates with increasing incident laser intensity; we obtain values ‖α2‖=70 cm W−1 and ‖n2‖≊0.2 cm2 kW−1. At room temperature we do not observe a well-defined exciton; saturation of the residual interband absorption occurs at much higher intensity, and it is found to be obscured by strong thermal effects.