Stability ef electron trajectories in free-electron lasers with an axial magnetic field is analysed in this paper. The results show that in the case of non-cyclotron-resonance( ),the trajectories are instable if the condition( )/(2ww)2= 1 is satisfied, while in the case of cyclotron-resonance ( ), the trajectories are always stable if the initial perpendicular velocities of electrons are small. On the other hand, oscillation amplitudes of the parallel velocities of electrons depend on the ratio Bw/B0. The smaller the ratio, the smaller the oscillation amplitudes.