  We study the general properties of axially symmetric dissipative
configurations under the shear-free condition. The link between the magnetic
part of the Weyl tensor and the vorticity, as well as the role of the
dissipative fluxes, are clearly exhibited. As a particular case we examine the
geodesic fluid. In this latter case, the magnetic part of the Weyl tensor
always vanishes, suggesting that no gravitational radiation is produced during
the evolution. Also (for the geodesic case), in the absence of dissipation, the
system evolves towards a FRW spacetime if the expansion scalar is positive.
