The mechanical response of giant liposomes to compression between two parallel plates is investigated in the context of an artificial actin cortex adjacent to the inner leaflet the bilayer. We found that nonlinear membrane theory neglecting the impact of bending sufficiently describes the mechanical response of liposomes consisting of fluid lipids to compression -whereasthe formation of an actin cortex or the use of gel-phase, lipids generally leads to substantial stiffening of the shell. Giant vesicles are gently adsorbed on glassy surfaces and are compressed with tipless cantilevers using an atomic force microscope. Force-compression curves display a nonlinear response that allows us to determine the membrane tension sigma(0) and the area compressibility modulus K-A by computing the contour of the vesicle as a function of the compression depth. The values for K-A of fluid membranes correspond well to what is known from micropipet-suction experiments and computed from monitoring membrane undulations. The presence of a thick actin shell adjacent to the inner leaflet of the liposome membrane stiffens the system considerably, as mirrored in a significantly higher apparent area compressibility modulus.