  We discuss the effect that small fluctuations of local anisotropy of
pressure, and energy density, may have on the occurrence of cracking in
spherical compact objects, satisfying a polytropic equation of state. Two
different kind of polytropes are considered. For both, it is shown that
departures from equilibrium may lead to the appearance of cracking, for a wide
range of values of the parameters defining the polytrope. Prospective
applications of the obtained results, to some astrophysical scenarios, are
pointed out.
