This paper introduces modelling and simulation of signal distortions as well as intensity noise induced by two-tone direct intensity modulation of semiconductor lasers for use in radio-over-fibre (RoF) systems. The study develops a large-signal modulation of semiconductor laser simulations in the regime of high-frequency modulation by counting lasers with high modulation bandwidth. The temporal and spectral characteristics of the modulated laser output are investigated. The temporal characteristics include the fluctuations in the modulated signal waveforms, while the spectral characteristics include the frequency spectrum of the modulation response, second-order harmonic distortion (HD2) and second- and third-order intermodulation distortions, IMD2 and IMD3, respectively, as wellas the relative intensity noise (RIN). The investigations are performed under three bias currents I$_b$ of 2, 5 and 10 times the threshold value I$_{th}$ over a wide range of modulation depth that covers regimes of small and large-signalmodulation and at modulation frequencies as high as 8 and 25 GHz with a spacing of 10 MHz. The dynamic range of the linearity of the investigated laser is evaluated in terms of spurious-free dynamic range (SFDR). The results showthat the nonlinear distortions increase as modulation depth increases. The highest distortion levels are observed when the modulation frequency approaches the laser relaxation frequency. The low-frequency RIN increases as themodulation depth and/or bias current increase and it has levels which are smaller when the modulation frequency is 8 GHz than when it is 25 GHz.