A description is made of electron trajectories in a magnetic field consisting of helical wiggler and a uniform axial guide field. The explicit motion of particles for which the quadratic approximation to the Hamiltonian was carried out in some previous publications is now presented. The transverse position as a function of time is essentially the superposition of three circular motions of different frequency; one corresponds to the fixed point, the second to the cyclotronic motion, while the third is a very slow motion of the center of gyration. Electrons in this model swept out the x - y plane with elliptical and circular orbits that characterize the group I, the normal and reversed-field group-II configurations. Several illustrative examples are discussed in detail.