Bloch–Bloembergen–Slonczewski (BBS) equation is established by extending Bloch–Bloembergen equation, and it is used to study magnetization oscillation in the free magnetic layer of a magnetic tunneling junction. Since both short–wavelength magnon excitation and spin–transfer torque are taken into account in the BBS equation, it is distinguished from Landau–Lifshitz–Gilbert–Slonczewski equation. The macro–spin BBS model predicts that the transverse relaxation time in free magnetic layer should be long enough, as compared with the longitudinal relaxation time, to achieve stable magnetization oscillation for spin–transfer torque oscillator application. Moreover, field–like torque favors the tolerance of fast transverse relaxation, which makes magnetic tunneling junction a better choice than spin valve for the spin–transfer torque oscillator application.