  Using a framework based on the $1+3$ formalism we carry out a study on
axially and reflection symmetric dissipative fluids, in the quasi--static
regime. We first derive a set of invariantly defined "velocities", which allow
for an inambiguous definition of the quasi--static approximation. Next we
rewrite all the relevant equations in this aproximation and extract all the
possible, physically relevant, consequences ensuing the adoption of such an
approximation. In particular we show how the vorticity, the shear and the
dissipative flux, may lead to situations where different kind of "velocities"
change of sign within the fluid distribution with respect to theirs sign on the
boundary surface. It is shown that states of gravitational radiation are not
{\it a priori} incompatible with the quasistatic--regime. However, any such
state must last for an infinite period of time, thereby diminishing its
physical relevance.
