The high‐field current‐field characteristics of Ga1−xAlxAs transferred‐electron‐effect devices for 0.2<x<0.4 have been measured under hydrostatic pressure, as well as the pressure dependence of the Hall coefficient in the range 0–15 kbar. From the critical pressure to suppress current instabilities and the Hall‐coefficient data, the energy positions of the L and X conduction‐band minima are derived for 0<x<0.45. The Γ‐L and Γ‐X energy separations for GaAs are determined to be 0.29±0.01 and 0.485 eV, respectively. The Γ‐X and Γ‐L crossover points are x=0.43 and 0.45±0.02, respectively. The alloy composition for velocity saturation is x=0.33, and the corresponding threshold field, as determined from a probe measurement, is 6.5±0.5 kV/cm.