In this article rue derive the basic equations of a nonlinear theory f
or binary mixtures of elastic materials in which the constituents may
have different temperatures. The independent constitutive variables ar
e the displacement fields, the first displacement gradients, the tempe
ratures of the constituents, and the temperature gradients. The basic
equations of the linear theory are established, and the displacement-t
emperature equations in the case of homogeneous and isotropic material
s are derived.