The hydrostatic-pressure coefficients of the bandgap energies for four different types of semiconductor heterojunction structures were obtained from photoluminescence measurements at 4K and pressures up to 4 kbar. The structures studied were n-type and p-type InxGa1-xAs/GaAs and n-type GaAs/GaPx As1-x strained-layer superlattices, n-type InxGa1-xAs/GaAs single strained quantum wells and an undoped GaAs/AlAs superlattice. The bandgap energies ranged from 1800 meV for the GaAs/ALAS structure to 1280 meV for the InxGa1-xAs/GaAs single strained quantum wells. Pressure coefficients for the InxGa1- As/GaAs and GaAs/GaPxAs1-x structures were found to be in the range of 10 to 12 meV/bar. However, the pressure coefficient of the luminescence energy from the GaAs/AlAs superlattice was found to be -2 meV/kbar. This negative pressure coefficient is consistent with the interpretation that the luminescence is due to a transition between the conduction-band X-point in the AlAs layers and the valence-band r-point in the GaAs layers.