The theory of mixtures has been a subject of intensive study in recent years. It is not our intention to survey the literature on mixtures and we give references only to papers which are relevant to our particular purpose. Certain ideas of nonlocality in continuum mechanics of a single phase medium have been studied by EDELEN [1], EDELEN & LAWS [2], EDELEN, GREEN & LAWS [3], and GREEN & LAWS [4]. In the present paper we apply some of these ideas to the theory of mixtures. As well as providing a theory of mixtures capable of dealing with nonlocal action, the point of view adopted here throws light on the theory when nonlocal action is excluded. We restrict attention in this paper to a mixture with a single temperature field. Fundamental equations are derived in sections 3, 4, including an entropy production inequality of global form for the mixture as a whole. As a particular application of the present theory we study, in sections 5, 6, the well discussed problem of a mixture of v ideal fluids and obtain results which are similar to those of MOLLER [5] * and GREEN & NAGHDI [6, 7], although there are some differences in interpretation as far as energy flux is concerned. In section 7 the global entropy inequality is replaced by one of a form used by MOLLER [5]. Results for ideal fluids, using this inequality, are shown to be identical with those obtained in sections 5, 6. An incompleteness in the constitutive discussions of GREEN & NAGHDI, pointed out by Mi]LLER [5] and others, was remedied by GREEN 8~ NAGHDI [6] and later given further justification by the same authors [7]. As shown by GREEN & NAGHI)I [6, 8] this incompleteness is only of significance if individual values of the partial stresses and diffusive forces are required, since the "missing" terms make no contribution to the equations of motion and energy, and to the total stress. The work of the present paper provides further understanding of these questions. In particular, in section 8, we give another explanation of the terms which, for completeness, GREBN & NAGnDI [6] suggested should be added to constitutive equations, and which have the property described above.