Classically, the description of a fluid is assumed to be governed by the usual variables: density, temperature, and velocity. Here it is postulated that such a system requires supplementary variables, namely, the heat flux vector and the viscous part of the pressure tensor. Starting from this hypothesis, a general theory of thermoviscous fluids is proposed. Balance equations and constitutive equations necessary to its description are given. Restrictions on the form of the constitutive equations are placed by the second law. The relaxation times associated with the various dissipative fluxes are interpreted in terms of the theory of fluctuations. This is achieved by extending Einstein's theory of fluctuations. The corresponding expressions for the second moments and the time correlations of the fluctuations of the dissipative fluxes are derived. In the limit of vanishing relaxation times, the classical results are recovered. © 1982 American Institute of Physics.