Spatial oscillations of the nonparaxial nonlaminar electron beams in periodic and quasiperiodic magnetic fields are considered. Both qualitative and numerical analysis confirm the conclusions previously made in the investigations of the more simple model of the paraxial and laminar electron beam. 
Thus, it is shown that in the vast domains of the beam parameters chaotic oscillations exist due to the resonance overlapping mechanism. 
In these domains the electron trajectories, instead of exponential deviation from the beam center, display large and irregular oscillations around it, so that the beam as a whole still remains in the limited space domain. Thus, the decline of nonlinear resonances suppresses the parametric instability of the beam, and enables the stable focusing of the beam. 
On the contrary to the case of the laminar and paraxial beam, the cases of nonlaminar and nonparaxial one show a great variety in the beam parameters and initial con- ditions leading to the spatial chaotic oscillations. Although the domains of stable oscillations in the nonparaxial nonlaminar case are confined to less area on the parameter plane than in the former case, chaotic oscillations occupy almost the whole space inside them.