The theory of laser oscillation with an intracavity sinusoidal modulation of the optical frequency is revisited and analyzed in the framework of general principles governing the properties of time-dependent periodic systems. It is shown that the two traditional and complementary descriptions of frequency modulation ͑FM͒ laser oscillation and pulsed FM mode-locking ͓S.E. Harris and O.P. McDuff, IEEE J. Quantum Electron. QE-1, 245 ͑1965͒; D.J. Kuizenga and A.E. Siegman, ibid. QE-6, 694 ͑1970͔͒ can be unified by means of a more general approach based on a Floquet analysis of the laser equations in presence of a periodic phase perturbation. Starting from a spatially extended model of intracavity laser frequency modulation for a homogeneously broadened two-level ring laser, the relevant Floquet modes and corresponding Floquet exponents governing the stability properties of the nonlasing state are derived as solutions of a nonlinear eigenvalue problem. Resonance phenomena, which occur when the modulation frequency is made close to an integer multiple of the cavity axial mode separation, explain the onset of FM laser oscillation and the transition to the pulsed FM mode locking closer to the synchronous modulation. In particular, the transition from FM laser oscillation to the pulsed FM mode locking is shown to be sharp and due to a crossing of the threshold curves of two distinct Floquet modes. The role of cavity dispersion on the transition is also investigated.