The work described in this paper, extends to finite magnetic fields, the study of the exceptionally large value of x(3) found for moderate radiation intensities close to resonance with interband transitions in Indium Antimonide (InSb). The intensity dependence of both interband magneto-absorption and dispersion, for transitions between individual identifiable Landau levels, was examined experimentally. The intensity dependence of the magnetic field dependent oscillations, in non-resonant interband Faraday rotation, provided a sensitive technique for the study of changes in magneto-dispersion. An intensity induced rotation corresponding to a maximum refractive index of - 9 x 10-5 W-1 (x(3) ca 10-1 esu, or ca 10-9 m2 V-2) was observed. This effect exhibited resonant enhancement as the pump photon energy approached that of both the fundamental bandgap and an acceptor transition and showed saturation at increased incident intensity. The effect was determined to be primarily the result of the blocking of the interband transition by photoexcited carriers. The intensity dependence of the magneto-absorption showed saturation effects for radiation intensities as low as 6 W cm-2, with the peak absorption coefficients being reduced by nearly a factor of two for an order of magnitude increase in intensity. The results are compared with two new microscopic models, the direct saturation model, which assumes a non-thermal distribution of the photoexcited carriers, and the dynamic Burstein-Moss model, which assumes a thermalised distribution. Comparison with experimental results yields values for the electron-hole dephasing time of T2 of the order of 3 ps and an interband relaxation time of TI of the order of 100 ns. In thin samples, a value of T1 some two orders of magnitude shorter was obtained, due to carrier diffusion and rapid surface recombination.