We report on Monte Carlo simulations of low-field hole transport at 77 K in InGaAs-AIGaAs quantum wells of different widths and alloy compositions. The valence subband structure is obtained using a k . p method within the infinite well approximation, which accounts for mixing between heavy and light hole states. The effects of alloy, impurfiy and phonon scattering are included in the transport simulations. Although the infinite well approximation is only expected to be reliable for barriers with an aluminium fraction greater than about 0.4. for which the heavy hole well is sufficiently deep, the resuits show good agreement with experimental measurements for a finite 90 8, Ino,,,G~,,,P.-GaAs quantum well. Astudy of hole transport in 908, In,Ga,-,& wells (0.10 < x < 0.25) predicts a mobility which increases with indium concentration since the reduction in the effective mass of the highest HHi valence subband due to strain more than compensates for the greater alloy scattering rate. An analysis of wells wah 18% indium content and widths in the range 50-1508, indicates a general increase in hole mobility with well width but with a local minimum around 908, due to intersubband scattering from the HHi subband to the heavier HHZ subband.