We discuss the effect that small fluctuations of density and local anisotropy (principal unequal stresses) may have on the occurrence of cracking in spherical compact objects having a non local and local politropic equations of state. A non local equation of state provides, at a given point, the radial pressure not only as function of the density at that point, but its functional throughout the enclosed distribution. It is shown that departures from the equilibrium may lead to the appearance of cracking and it seams to be related not only to fluctuations on the local anisotropy but also to the density. We have found that these fluctuations should have the same sign and the effect of the perturbations in density qualitatively different to the variations in anisotropy.