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This paper studies the coherence of the radio-frequency (RF) beat note between the two frequencies emitted by a two-eigenstate solid-state laser operating in pulsed regime. Depending on how the pulsed operation regime is obtained-passive Q switching using a saturable absorber or resonant amplitude modulation using pump-power modulation-we show theoretically and experimentally that the RF beat note loses or maintains its coherence from pulse to pulse. Namely, RF coherence is shown to be lost when the laser intensity vanishes between pulses, while it can be maintained if a slight amount of intensity remains inside the cavity between pulses. We give experimental demonstrations of these results for both Nd:YAG and Er-Yb:glass two-frequency pulsed lasers, in connection with applications to lidar-radar systems.