For slowly rotating fluids, we establish the existence of a critical p
oint similar to the one found for nonrotating systems. As the fluid ap
proaches the critical point, the effective inertial mass of any fluid
element decreases, vanishing at that point and changing sign beyond it
. This result implies that the first-order perturbative method is not
always reliable to study dissipative processes occurring before relaxa
tion. Physical consequences that might follow from this effect are com
mented on. (C) 1998 American Institute of Physics.