We report a comprehensive investigation of the local structure around As in thin InAs x P 1Ϫx strained layers in InAs x P 1Ϫx /InP superlattices by fluorescence-detected x-ray-absorption fine structure; seven superlattice samples are studied as a function of composition, and compared to six unstrained, bulk samples of similar composition. Contributions up to the third coordination shell around As are clearly visible in the spectra, and are analyzed taking into account important multiple-scattering contributions. Results show that structural modifications due to tetragonal distortion appear mainly in the second and third coordination shells, while nearest-neighbor bond lengths remain closer to the values in unstrained bulk alloys. This implies that in semiconductor alloys tetragonal strain accommodation is mainly obtained through bond-angle distortions, in analogy to the situation in bulk pseudobinary alloys. A model which combines macroscopic elastic theory and the known local structure in bulk pseudobinary alloys is presented, and is found to fit the data very well.