The response of nanolasers to direct current modulation has been analyzed in both the small-signal and large-signal regimes. Calculations have been performed using rate equations which include the Purcell cavity-enhanced spontaneous emission factor F and the spontaneous emission coupling factor β. It is observed that in general increased F and β reduce the 3-dB direct current modulation bandwidth. Conditions are identified where the peak modulation response at resonant frequencies 35 and 30 GHz can be achieved. For both small- and large-signal regimes, modulation bandwidth of approximately 55 GHz can be achieved.