The authors describe the molecular beam epitaxy of relaxed, nominally undoped In0.75Ga0.25As–In0.75Al0.25As quantum well structures grown on InP substrates. The maximum two-dimensional electron density is 2 × 1011cm−2, with a peak mobility of 2.2 × 105cm2 V−1s−1 at 1.5K. In high magnetic field, the electron g-factor was shown to have a magnitude of 9.1 ± 0.1 at Landau-level filling factor of 4. The Rashba coefficient, determined from the analysis of the magnetoresistance at high Landau-level filling factor (>12), is 1 × 10−11eVm. The mobility is sufficiently high in these two-dimensional electron gases that spin-orbit effects are observed up to 4.2K. The interface asymmetry, defined as the difference between the wavefunction penetration into the upper and lower In0.75Al0.25As quantum barriers, makes no contribution to the Rashba spin-orbit coupling parameter in this system. Quantum wires defined in these two-dimensional electron gases using insulated, split surface gates show clear quarter-integer quantized conductance plateaux at exactly 0.25(2e2 / h) and 0.75(2e2 / h) in nonequilibrium transport. In0.75Ga0.25As may have important application as an alternative field effect transistor channel to silicon, and the large electronic g-factor and Rashba spin-orbit coupling parameter make this material combination suitable for exploring spin related phenomena in one-dimensional systems.