The phase structures of Nambu-Jona-Lasinio models with one or two flavors are investigated at nonzero values of and H, where H is an external magnetic field and is the chemical potential. In the phase portraits of both models there arise infinitely many massless chirally symmetric phases, as well as massive ones with spontaneously broken chiral invariance, reflecting the existence of infinitely many Landau levels. Phase transitions of first and second orders and a lot of tricritical points have been shown to exist in phase diagrams. In the massless case, such a phase structure leads unavoidably to the standard van Alphen-de Haas magnetic oscillations of some thermodynamical quantities, including magnetization, pressure and particle density. In the massive case we find an oscillating behavior not only for thermodynamical quantities, but also for a dynamical quantity as the quark mass. In addition, in this case we have nonstandard, i.e., nonperiodic, magnetic oscillations, since the frequency of oscillations is an H-dependent quantity.

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