Room-temperature angle-dispersive x-ray diffraction measurements on zircon-type TbVO₄ and CeVO₄ were performed in a diamond-anvil cell up to 50 GPa using neon as a pressure-transmitting medium. In TbVO₄, we found at 6.4 GPa evidence of a nonreversible pressure-induced structural phase transition from zircon to a scheelite-type structure. A second transition to an M-fergusonite-type structure was found at 33.9 GPa, which  is reversible. Zircon-type CeVO₄ exhibits two pressure-induced transitions: first, an irreversible transition to a monazite-type structure at 5.6 GPa and, second, at 14.7 GPa, a reversible transition to an orthorhombic structure. No additional phase transitions or evidences of chemical decomposition are found in the experiments. The equations of state and axial compressibility for the different phases are also determined. Finally, the sequence of structural transitions and the compressibilities are discussed in comparison with other orhtovanadates and the influence of nonhydrostaticity commented.