In this thesis, we have described an extension to R-Matrix with Time Dependence (RMT) theory and associated codes that allows full modelling of ultrafast double ionisation processes. This approach extends the capability of R-Matrix methods to model ionisation and scattering processes in many electron problems. Previously, all R-Matrix methods for double ionisation were either time-independent (e.g IERM) (and hence incapable of modelling the ultrafast processes of contemporary interest), or incapable of representing configuration space to the extent necessary to model double ionisation wavepackets (e.g. traditional RMT). This thesis demonstrates the feasibility of application of the RMT formalism to the study of double ionisation processes through application to for two and three electron systems.