We have measured the Landau-level spin-splitting of two-dimensional electrons in the composite InAs/InGaAs channels of two InAs/InGaAs/InAlAs heterostructures with different alloy compositions by magnetotransport and THz magneto-photoconductivity in magnetic fields up to 10 T. The structures differ importantly in the mobility of the channel, the electron density and the composition of the barriers. The magnitudes of the experimental g-factors for B along the quantization axis and their anisotropies are larger by at least a factor of 2 than the corresponding calculated single particle values. The angular dependence of many-body exchange contributions and the effects of broadening of Landau–level densities of states are necessary for understanding this behaviour. We find evidence for a marked decrease of the exchange contribution at low perpendicular magnetic fields in the higher mobility sample from coincidence measurements, but no indications of such behaviour in the lower mobility sample.