Studies of the spectral content and stability of an intracavity second-harmonic ring laser show that single-mode cw operation is stable against amplitude-modulated fluctuations, whereas frequency-modulated fluctuations are undamped. cw operation tends to single longitudinal mode output under very general conditions provided frequency modulation is not introduced. Multimode frequency-modulated cw operation can be achieved. Methods for producing an anti-mode-locked laser and a frequency-modulated laser are described. However, the presence of an intracavity spectral filter will remove frequency modulation. The importance of a spectral filter to restrict the fundamental frequency to the phase-matched bandwidth of the doubler is emphasized.