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The high pressure behavior of negative thermal expansion materials continues to be of interest, as their potential use in controlled thermal expansion composites can be affected by irreversible pressure-induced phase transitions. To date, it is not possible to predict the high pressure behavior of these compounds, necessitating measurements on each composition. In this work, high pressure synchrotron powder X-ray diffraction studies of Cr2Mo3O12 and Y2Mo3O12 were conducted in a diamond anvil cell. Chromium molybdate, which adopts the monoclinic P21/a structure under ambient conditions, was found to not undergo any crystalline-crystalline transitions up to 8.9 GPa. The orthorhombic ambient pressure polymorph of yttrium molybdate was found to undergo a phase transition to the monoclinic P21/a scandium tungstate structure below 0.13 GPa. This structure is frequently observed for related materials at low temperatures, but has never been reported for Y2Mo3O12. No additional changes in this material were observed up to 4.9 GPa. The fact that the monoclinic polymorphs of these materials do not undergo phase transitions within the studied pressure range makes them unique among A2M3O12 materials, as most isostructural compositions undergo at least one phase transition to crystalline high pressure phases.