Summary: The existence of vector fields which commute with the vector field of the initial system and are defined in the entire phase space is discussed. The phase fluxes of these fields are well-known to be symmetry groups of a dynamic system, since they map the set of all its solutions into itself. Obstacles to the existence of non-trivial symmetry groups are the generation of a large number of non-degenerate periodic solutions, and the transversal intersection of asymptotic surfaces. The symmetry groups of systems of a “normal” type, which play an important part in perturbation theory, are examined in detail. The general results are applied, in particular, to Hamiltonian systems. It is shown that the equations of rotation of a heavy asymmetric rigid body with a fixed point do not have a non-trivial symmetry group if the centre of mass of the body is not the same as the point of suspension. In particular, there is no supplementary many-valued analytic integral which is independent of the classical energy and area integrals.