We studied the effects of high pressure on the crystalline structure of scheelite-type CdMoO₄ and EuMoO₄. We found that the compressibility of the materials is highly nonisotropic, with the c-axis being the most compressible one. We also observed clear evidence of a structural phase transition at 12 GPa (CdMoO₄) and 8.8 GPa (EuMoO₄). The high-pressure phase has a monoclinic structure similar to M-fergusonite. The transition is reversible, and no volume change is detected between the low- and high-pressure phases. The results contradict early x-ray diffraction studies carried out in CdMoO₄ and are compared with those obtained previously in isomorphic molybdates. Finally, the equation of state for both compounds is also determined