  We use an orthonormal frame approach to provide a general framework for the
first order hyperbolic reduction of the Einstein equations coupled to a fairly
generic class of matter models. Our analysis covers the special cases of dust
and perfect fluid. We also provide a discussion of self-gravitating elastic
matter. The frame is Fermi-Walker propagated and coordinates are chosen such as
to satisfy the Lagrange condition. We show the propagation of the constraints
of the Einstein-matter system.
