Magnetic properties of ${\text{Fe}}_{64}{\text{Ni}}_{36}$ and Fe-Pt Invar alloys under high pressure have been investigated through x-ray magnetic circular dichroism (XMCD) up to 12 GPa at ambient temperature and superconducting quantum interference device magnetometer up to 1 GPa for different isotherms, from 10 to 300 K. Results obtained with both techniques on Fe-Pt samples can be well interpreted through the $2\ensuremath{\gamma}$-state interpretation of the Invar effect. For the ${\text{Fe}}_{64}{\text{Ni}}_{36}$ alloy, the relative evolution of the iron magnetic moment at 300 K, measured through XMCD, shows the existence of a plateau between 4 and 10 GPa, also expected within this approach. In the low-pressure range, the evolution of magnetization indicates that the itinerant character of Fe-Ni alloys may affect the transition.