In this paper we consider global bifurcation from infinity in nonlinearizable Dirac problem with a spectral parameter contained in both boundary conditions. We prove the existence of two families of unbounded components of the set of nontrivial solutions to this problem, which bifurcate from asymptotic intervals and contained in classes of vector- functions possessing oscillatory properties of the eigenvector-functions of the corresponding linear Dirac problem in the neighborhood of these intervals.