In the context of the Muller-Israel-Stewart second-order phenomenologi
cal theory for dissipative fluids, we analyse the effects of thermal c
onduction and viscosity in a relativistic fluid, just after its depart
ure from hydrostatic equilibrium, on a time scale of the order of the
relaxation times. Stability and causality conditions are contrasted wi
th conditions for which the 'effective inertial mass' vanishes.