In this paper we theoretically investigate the influence of the injection of a so-called holding beam - a CW beam at the transparency wavelength of the gain medium on the direct modulation properties of semiconductor lasers. Both the small-signal and the large-signal behaviour are investigated. The influence of the holding beam is studied using a simple rate equation model. From the solution of the rate equations it follows that the injection of the holding beam doesn't increase the modulation bandwidth or resonance frequency itself, but that it results in a significant increase of the damping of the relaxation oscillations. Furthermore, it is shown that the chirp (both the adiabatic and dynamic chirp) will be significantly reduced. A few numerical examples - calculated with our CLADISS software - are given to show that the modulation response at not too high bias levels can be significantly improved when a holding beam is applied. For direct, large signal modulation, the injection of a holding beam leads to significantly reduced transient effects and reduced chirping, even at low bias.