We have investigated the intrinsic modulation response ofGaxIn1-xP/AlGaInPquantum well lasers. The differential gain resulting from the measurement of the frequency response, is in good agreement with calculations based on a 6-bandkp-theory and direct measurements of the optical gain. We find a maximum value of3.8×10−16cm2for a strongly compressively strained sample, which is less than in InGaAs lasers according to the larger effective masses. The maximum bandwidth we observed is 9.3 GHz at −3 dB. We show that the bandwidth is limited by catastrophic optical damage and not by intrinsic mechanisms. ©1997 American Institute of Physics.