  We investigate the conditions for the (in)stability of the isotropic pressure
condition in collapsing spherically symmetric, dissipative fluid distributions.
It is found that dissipative fluxes, and/or energy density inhomogeneities
and/or the appearance of shear in the fluid flow, force any initially isotropic
configuration to abandon such a condition, generating anisotropy in the
pressure. To reinforce this conclusion we also present some arguments
concerning the axially symmetric case. The consequences ensuing our results are
analyzed.
