A study is made of the general-covariant equations of motion of Trautman for a particle interacting with an external field. It is shown that in the general case the relativistic equations of motion are not solvable for the acceleration four-vector but have the form aik(Dukds) = Fi. Formulas are given foraik and Fi by means of which they can be calculated in terms of the known Lagrangian. Examples are given of the motion of a particle in tensor fields of rank zero, one, and two. The Hamilton-Jacobi equation for an arbitrary interaction law is constructed.