High‐pressure measurements of thermionic emission (TE) and of resonant tunneling in Ga1−xAlxAs/GaAs double barrier structures are reported, wherex=1 or 0.33. Forx=1, TE in a structure with a very narrow well yields a direct measurement of ∼150 meV for the &Ggr;‐X barrier height, and a shift of ∼−11 meV/kbar. For a structure with a well width of ∼70 A˚ and barriers of ∼40 A˚, negative differential resistance (NDR) is observed, which is suppressed at a pressure of ∼8 kbar, when the height of the &Ggr;‐X barrier is approximately equal to the confinement energy of the state in the well. Forx=0.33, and in samples with spacer layers, the same criterion for suppression of the NDR applies as forx=1. When spacer layers are absent, anomalies occur in the variation of the first NDR resonance with pressure, and for sufficiently large samples, the threshold for loss of NDR is much lower than expected. The anomalous behavior is related to the higher concentration of impurities in the barriers. The low‐pressure threshold of the anomaly, and the dependence of the anomaly on sample size, suggest that impurity correlation may play a significant role in the suppression of NDR. At low pressures, or in the absence of anomalies, the pressure dependence of the peak and valley currents of all resonances which are always in the range −1% to −3%/kbar, indicates that the &Ggr; profile controls the tunneling, through the pressure dependence of the effective mass.