EXAFS spectroscopy experiments have been carried out on quartz-like alpha-GaAsO4 and alpha-AlAsO4 at high pressure and room temperature. It has been shown that these materials exhibit two structural phase transitions; the first transition to a high pressure crystalline form occurs at 9 GPa and is reversible upon decompression, whereas the second transition occurrs at higher pressures and is irreversible. In alpha-GaAsO4, EXAFS measurements agree with the predicted transition from four-to sixfold coordination of oxygen atoms around the cations, but the two local coordination transformations are not dissociated; in fact, both As and Ga atoms exhibit a coordination change at the onset of the first phase transition, the rate of transformation being significantly higher for Ga atoms. In both cases, the average bond length increases very rapidly with pressure thus yielding the first compression stage after the transition. In the second stage, the average bond lengths increase slowly, ultimately reaching six-fold coordination above 28 GPa and 24 GPa for As and Ga respectively. The behaviour of the As K-edge EXAFS is the same for both compounds, and enables us to link the behaviour of Ga and Al atoms. The local transformations are well described and a direct link with phosphate berlinites seems timely.