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Pump and probe measurements with femtosecond resolution are performed on a gain-clamped semiconductor optical amplifier, a structure that contains a lasing mode. The corresponding relaxation oscillations are observed in the temporal gain recovery of the amplifier. The current dependence of the oscillations is well reproduced by a small-signal analysis of the laser rate equations. The gain recovery can be very fast, we measure damping rates of up to 40 GHz.