A fairly general scheme for gravitational theories is given, which combines tetrad field theories with bimetrical theories. General Relativity is included in this class and is (essentially in a unique manner) characterized by requiring form invariance of field equations with regard to coordinate transformations and to space-time depending Lorentz rotations of the tetrad. Dropping the first of these conditions leads to gravitational theories based on a bimetric formalism (ROSEN-PAPAPETROU-KOHLER), dropping the second gives tretad gravitational theories (EINSTEIN-MAYER, PLEBAŃSKI-PELLEGRINI). Dropping both conditions leads to a large class of partly known (TREDER) and partly new theories. For a particular subset of this class it is shown that redshift and light deflection can easely be given the values following from General Relativity, the situation is similar for the perihelion motion. It is emphasized that an approach of the type considered here should not be considered as leading to gravitational theories comparable in significance with theories based on stronger invariance principles, such as General Relativity in particular.