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This paper deals with a continuum model of rigid superconductors. It is assumed that their property of shifting to the superconductive state for suitable values of temperature and magnetic field is due to a vectorial internal variable, related to the superelectron current by a linear constitutive law. The compatibility of the model with the second law of thermodynamics is investigated. The propagation of thermo-electromagnetic waves through a one-dimensional conductor is analyzed as well. Comparison is made with different continuum approaches which may be found in the literature.