The mobility of electrons, µe, and holes, µp, in epitaxial layers of In1-xGaxAsyP1-y grown lattice matched to InP are presented as a function of composition, of temperature and of pressure. A strong downward bowing in µe and µp is observed as a function of y at room temperature. The temperature, T, variation of µe and µp shows that ionized impurity scattering is light but a strong scattering proportional to T-1/2 exists. The pressure variation of µe indicates that this is due to alloy scattering rather than to space-charge scattering. The alloy scattering potentials ΔUe in n-type, and ΔUp p-type material both reach a maximum near the centre of the alloy range where ΔUe≃0.7 eV and ΔUe≃0.3 eV. A simple model suggests ΔUp may be associated with fluctuations in the ionization potential, while ΔUe may be associated with band gap fluctuations.