The output of a laser-diode-pumped Nd:YAG laser with an intravcavity-doubling crystal exhibits large-amplitude fluctuations and longitudinal-mode instabilities. The results of an experimental and theoretical investigation of these instabilities are described. The instabilities arise from coupling of the longitudinal modes of the laser oscillator by sum-frequency generation in the nonlinear crystal. A rate-equation theory of a multilongitudinal-mode laser oscillator with an intracavity-doubling crystal is presented that includes terms modeling the sum-frequency and frequency-doubling processes.