The HP behaviors of a natural chabazite and of SAPO-34 as synthesized wereinvestigated by means of in-situ synchrotron X-ray powder diffraction, with the aim of understandingthe role of the framework/extraframework content on the response to pressure. Compressibility wasdetermined with silicon oil, as non-penetrating P-transmitting medium, up to 7.6 GPa and 4.5 GPafor chabazite and SAPO-34, respectively. The isothermal Equation of States (EoS), refined with athird-order (chabazite) and a second order (SAPO-34) Birch-Murnagan EoS, yielded the followingparameters: V0=839(1) Å3, K0 = 41(3) GPa, Kp = 11(2) GPa, and V0=2439(4) Å3, K0 = 29(1)GPa, for chabazite and SAPO-34, respectively. These results indicate that chabazite is lesscompressible than SAPO-34. This is mainly ascribed to the more complex and hindering extraframeworkcontent of the natural sample. No complete structural refinements of the powderpatterns were performed, but the compressibility of these materials with CHA topology wastentatively interpreted on the basis of the deformation mechanism observed in the structurallyrelated zeolite levyne. The comparison between the volume decrease induced on chabazite by highpressure and by high temperature indicates that this zeolite is much more flexible undercompression than upon dehydration.