  The full set of equations governing the evolution of self--gravitating
spherically symmetric dissipative fluids with anisotropic stresses is deployed
and used to carry out a general study on the behaviour of such systems, in the
context of general relativity. Emphasis is given to the link between the Weyl
tensor, the shear tensor, the anisotropy of the pressure and the density
inhomogeneity. In particular we provide the general, necessary and sufficient,
condition for the vanishing of the spatial gradients of energy density, which
in turn suggests a possible definition of a gravitational arrow of time. Some
solutions are also exhibited to illustrate the discussion.
