A time-dependent density matrix approach is used to investigate the effects of strong laser fields on the ionisation dynamics of complex atomic systems. In particular, two-step ionisation of neon and lithium with autoionising state (AIS) resonances are investigated and the effects of the resonances on the ion yields is determined. The stochasticity of a free-electron laser (FEL) pulse due to phase fluctuations is also modelled by using the phase diffusion model to obtain field-averaged time-dependent density matrix equations. A rate equation method is also investigated and analysed for reliability. One of the main advances developed in this work is the use of the density matrix method to investigate two-electron continuum states. For the neon system, the dependence of the branching ratios of singly and doubly ionised neon on the field intensity and duration is investigated. The rate equation method was also developed for this system in order to test its applicability. The possibility of single-colour AIS-AIS resonances in lithium is also investigated. To the author’s knowledge, no such system has been examined either theoretically, or experimentally. Thus, this work provides a first investigation into two new topics.