The evolution of a Friedmann-Robertson-Walker universe filled with a viscous simple fluid is analysed. At variance with other treatments the authors' approach complies with relativistic causality since dissipative signals travelling at superluminal speeds are forbidden. This is because use is made of the extended thermodynamics theory of irreversible processes instead of the conventional one. As a consequence some novel results arise. In particular, the initial de Sitter phase of the deflationary universe does not occur. Likewise, the generalized second law of thermodynamics is studied within this context.