The possibility for a description in General Relativity of the motion of a particle subject to the action of different fields (f.i. electromagnetic field and nuclear field) in addition to the gravitation by means of a variational principle is examined. The principle consists in a generalization of the variational principle used in Special Relativity and coincides, for a free particle subject to the gravitational field only, with the well known principle of the geodesics. The formalism is extended to include also pseudotensorial fields of interest for the elementary particle physics.