We have used ultraviolet and x-ray photoelectron spectroscopy to study the strain dependence of the valence-band offset (VBO) in situ for binary arsenide compound semiconductor heterojunctions grown by molecular beam epitaxy; i.e., we have measured the VBO of InAs/GaAs, InAs/AlAs, and AlAs/GaAs(100) heterojunctions as it changes when these heterojunctions are pseudomorphically strained to lattice constants ranging from 5.653 Angstrom (GaAs) to 6.058 Angstrom (InAs). Intermediate lattice constants have been realized by using fully relaxed InxGa1-xAs buffer layers as virtual substrates. The spectrum of two distinct core-levels, one from either side of the coherently strained junction, monitors the energetic alignment across the junction. To establish the band offset, one has to know in addition the binding-energy separation of the core-level to the respective valence-band maximum (VBM) for each of the junction’s two components and corresponding to their correct bulk strain state. Here, we have recorded valence-band and core-level spectra of strained "bulk" samples to determine this energy difference experimentally. We have accounted for the true shape of the density of states near the VBM by using results of k . p theory, thus avoiding a full pseudopotential calculation. GaAs/InAs and AlAs/InAs heterojunction VBOs are heavily strain dependent. For example, one can alter the GaAs/InAs VBO by 480 meV on going from the GaAs to the InAs lattice constant, the InAs VBM being 0.04+/-0.10 eV lower than the GaAs VBM when InAs is strained to the GaAs lattice constant and 0.52+/-0.10 eV lower when the strain is vice versa. The AlAs/InAs heterojunction VBO changes from +0.29+/-0.11 eV (type-I), when InAs is strained to AlAs, to -0.10+/-0.17 eV (type-II) for the opposite case. The AlAs/GaAs heterojunction VBO is independent of strain within our limits of accuracy. The results are compared with recent theoretical data, both "model" theories and self-consistent calculations, shedding some light on the features that are important for the band alignment at polar heterojunctions. The results can be interpolated in a straightforward manner to estimate the VBO for the more realistic case of heterojunctions built up of any two ternary arsenide compounds strained to any reasonable lattice constant.