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In this paper, we present a numerical study to determine the feasibility of exciting and sustaining stable magnetization oscillations in magnetic nanocontact devices subjected to the combined action of a spin-polarized current and a perpendicular anisotropy field when no external field is applied. A systematic numerical analysis of the properties exhibited by such spintronic oscillators is carried out by means of a micromagnetic framework. The study reveals a nonlinear behavior of the excited frequency as the anisotropy field strength is varied. More noteworthy, full-scale investigations result in a hysteretic dependence of the excited frequency on the applied current together with the existence of two kinds of precessional spin-wave modes: an anisotropic radially propagating mode and a gyrotropic motion of a magnetic vortex-core.