The modulation properties of an injection-locked semiconductor laser are investigated using the rate equation formalism. Intensity and phase modulations (IM and PM) are analyzed throughout the locking range where the locked laser is stable. The relaxation oscillation resonance in the IM and PM frequency responses can be dramatically reduced by tuning the injected power and the frequency difference between the master laser and the free-running slave laser. The power spectra under direct modulation are derived throughout the stable locking range. The spreading of the harmonics of the modulated locked laser is strongly affected by the frequency detuning, the injected power, and the injected current modulation. Measurements illustrating the theoretical results are also presented.