<p>REE orthoarsenates and orthophosphates are common accessory minerals characterized by the general chemical formula REEXO<sub>4</sub>, where REE represents one of the lanthanides (La-Lu series), Y, Sc, Ca or Th, whereas X stands for As, P or Si. In the framework of a long-term project on the high-<em>T</em>/high-<em>P</em> crystal-chemistry and phase-stability of REE-bearing minerals, the high-pressure behavior of chernovite-(Y) (nominally YAsO<sub>4</sub>), xenotime-(Y) (nominally YPO<sub>4</sub>) gasparite-(Ce) (nominally CeAsO<sub>4</sub>) and monazite-(Ce) (nominally CePO<sub>4</sub>), has been studied. Chernovite-(Y) and xenotime-(Y) show a HREE- (Gd-Lu series) and Y-enrichment, and the same tetragonal symmetry (space group <em>I</em>4<sub>1</sub>/<em>amd</em>), whereas gasparite-(Ce) and monazite-(Ce) share the same LREE (La-Eu) enrichment and monoclinic cell (space group <em>P</em>2<sub>1</sub>/<em>n</em>). All these minerals occur at Mt. Cervandone (Western Alps, Italy), a renowned Alpine REE-bearing mineral deposit. The crystal chemistry of the four minerals has been studied via EPM-WDS analysis. Excluding gasparite-(Ce), which formation is bound to the replacement of the mineral synchisite-(Ce) (CaCe(CO<sub>3</sub>)<sub>2</sub>F), a sensible enrichment in Gd and Ho is observed. Moreover, the majority of the chernovite-(Y) show a variable amount of ThO<sub>2</sub>, up to 13 wt%, and phosphorous as substitute for arsenic in almost every proportion. In the case of the monoclinic series between monazite-(Ce) and gaparite-(Ce), no solid solution has been observed. Experiments at high-pressure were performed by in situ synchrotron X-ray diffraction using a diamond anvil cell. The high-pressure behavior of single crystals of xenotime-(Y), gasparite-(Ce) and monazite-(Ce) has been studied up to ~20 GPa, whereas that of chernovite-(Y) has been studied by powder diffraction up to 8.20(5) GPa. A II-order Birch-Murnaghan equation of state was fitted to the <em>V</em>-<em>P</em> data, within the phase stability field of the minerals, yielding the following bulk moduli: <em>K</em><sub>P0,T0</sub> = 125(3) GPa (&#946;<sub>V</sub><sub>0 </sub>= 0.0080(2) GPa<sup>-1</sup>) for chernovite-(Y); <em>K</em><sub>P0,T0</sub> = 145(2) GPa (&#946;<sub>V</sub><sub>0 </sub>= 0.0069(1) GPa<sup>-1</sup>) for xenotime-(Y); &#160;<em>K</em><sub>P0,T0</sub> = 106.7(9) GPa (&#946;<sub>V</sub><sub>0 </sub>= 0.0094(1) GPa<sup>-1</sup>) for gasparite-(Ce), <em>K</em><sub>P0,T0</sub> = 121(2) GPa (&#946;<sub>V</sub><sub>0 </sub>= 0.0083(1) GPa<sup>-1</sup>) for monazite-(Ce). <em>K</em>&#8217; = &#8706;<em>K</em><sub>V</sub>/&#8706;<em>P</em> = 4 (fixed) for all the minerals. Deformation mechanisms, at the atomic scale, were described on the basis of structure refinements. &#160;</p><p>Acknowledgments: This research was partly funded by the PRIN2017 project &#8220;Mineral reactivity, a key to understand large-scale processes&#8221; (2017L83S77).</p>