  The condition for the vanishing of the Weyl tensor is integrated in the
spherically symmetric case. Then, the resulting expression is used to find new,
conformally flat, interior solutions to Einstein equations for locally
anisotropic fluids. The slow evolution of these models is contrasted with the
evolution of models with similar energy density or radial pressure distribution
but non-vanishing Weyl tensor, thereby bringing out the different role played
by the Weyl tensor, the local anisotropy of pressure and the inhomogeneity of
the energy density in the collapse of relativistic spheres.
