This paper investigates theoretically the modification of dynamical properties in a semiconductor laser by a strong injected signal. It is found that enhanced relaxation oscillations are governed by the pulsations of the intracavity field and population at frequencies determined by the injected field and cavity resonances. Furthermore, the bandwidth enhancement is associated with the undamping of the injection-induced relaxation oscillation and strong population pulsation effects. There are two limitations to the modulation-bandwidth enhancement: Overdamping of relaxation oscillation and degradation of flat response at low frequencies. The injected-laser rate-equations used in the investigation reproduce the relevant aspects of modulation-bandwidth enhancement found in the experiment on injection-locked vertical-cavity surface-emitting lasers.