Classical thermodynamics of irreversible processes is a valuable tool for the study of suspensions, provided due care is devoted to the selection of internal variables. As a first example, the flow-induced anisotropic microstructure appearing in many a suspension is usually depicted by a vector, the orientation and length of which are submitted to a statistical distribution. We show how irreversible thermodynamics imposes restrictions on the time evolution of that structural internal variable (and consequently on the time evolution of its statistical distribution), and how this evolution is related to the elastic stress of the suspension. As a second example, we consider the possibility of a mean relative motion between the particles and the suspending fluid. Upgrading that relative velocity to the status of an internal variable, we analyse the consequences concerning the transport of mass, momentum and energy providing a link with the two-fluid model of suspensions, as well as with the well-known description of molecular mixtures.