In this paper, we present a theory for analysing the transient behaviour of injection-locked lasers with monochromatic injection, wherein homogeneously broadened wide-band lasers with injection are analysed. In addition to boundary conditions, the initial distribution of the laser and the monochromatic injection signal fields are necessary for solving the governing equations. The Maxwell–Bloch equations are reduced to a system of ordinary differential equations with the initial conditions. In this paper, two approximation methods are introduced. These approximations are named the De-satellite signal approximation and the finite number satellite signal approximation, respectively. The finite number satellite signal approximation is used to study the transient behaviour of the satellite signal around the laser frequency in injection-locked lasers. The results are in good agreement with the data published by the previous studies on this topic.