Following up the detailed three-dimensional analysis of the particle dynamics in a free electron laser with a helical wiggler and a uniform axial guide magnetic field, achieved by Rhimi et al. [1], we study the motion of the electrons in the neighborhood of the ideal trajectory. The normal modes <img src="http:/img/fbpe/bjp/v31n3/shace.gif">± of the quadratic Hamiltonian are analyzed numerically in both the normal and reversed-field configurations for different values of the ratio <img src="http:/img/fbpe/bjp/v31n3/20eq01.gif">w/<img src="http:/img/fbpe/bjp/v31n3/20eq01.gif">0. The electron trajectories are thus discussed. It is found that pseudo-circular and elliptic trajectories are characterizing both group-I and reversed-field group-II modes while the motion in the normal group-II mode is much more complicated.