In this note we consider the question of continuous dependence upon the initial data for solutions of the equations governing the motion of a linearly viscous compressible fluid. In particular, we show that provided the base flow lies in a certain class ~r and the perturbed flow in a class , / / then the solutions depend Hflder continuously on the initial data in the sense of F. JOHN [1]. The precise definition of the classes dr and ~ is given in (9) and (10). To establish this result we employ the weighted energy arguments of MURRAY & PROa~rrR [2] and MURRAY [3]. The uniqueness of the solutions is, of course, implied by the continuous dependence result. An earlier proof of the uniqueness was given by SERRIN [4] using a conventional energy approach. We assume that the fluid occupies a bounded region D of three space with a boundary dD which is smooth enough to allow applications of the divergence theorem. The density p, the components of the velocity v1 and the temperature T are well known to satisfy the system of equations