Fermion Fields in Theories of Gravitation

After an introduction to the formalism used throughout the paper there follows a concise presentation of the theory of fermion fields in one-tetrad gravitational theories. That presentation gives a hint to the construction of a bi-tetrad theory, the two tetrad fields being denoted by h^A_k and h?^A_k. The tetrad field h^A_k. gives the Riemannian metric g_kl while the tetrad field h?h^A_k is orthonormalized with respect to the flat metric a_kl. Specializing h?^A_k in such a way that they have the form δ^A_k in the preferred coordinates of Minkowski space and using a matter Lagrangian which contains these h?^A_k only by the anholonomic components of the metric Christoffel symbols, we obtain a dynamical energy momentum tensor which is equal to the canonical one. Then we consider the relations of the bi-tetrad theory to other theories which are only covariant with respect to global Lorentz transformations from the beginning. As an example we formulate the main relations of the two-component neutrino theory.