Third-harmonic microwave radiation of the BiSrCaCuO superconducting single crystal was studied. Two modes of microwave field-sample interactions were observed. In a weak field, a strong increase in the intensity of radiation after switching on a constant magnetic field, a hysteresis between opposite scan directions, and different harmonic amplitudes depending on the conditions of cooling (in the presence or absence of a magnetic field) were observed. These observations can be described by the generalized Ginzburg-Landau functional taking into account higher spatial derivatives of the order parameter. At a high intensity of incident waves, a magnetic field almost did not influence third-harmonic radiation, and, accordingly, hysteresis was absent. This is likely to be evidence that, at high powers, third-harmonic radiation arises as a result of generation of vortices under the action of a high-frequency magnetic field.