  We discuss the effect that small fluctuations of both local anisotropy and
energy density, may have on the occurrence of cracking in spherical compact
objects satisfying a polytropic equation of state. A systematic scheme to bring
the fluid configurations out of hydrostatic equilibrium is revisited. Various
models of polytropes are considered and it is shown that departures from
equilibrium may lead to the appearance of cracking for a wide range of values
of the parameters involved. Prospective applications of the obtained results to
some astrophysical scenarios are pointed out.
