Co-registered EEG and functional MRI (EEG/fMRI) is a potential clinical tool for planning invasive EEG in patients with epilepsy. In addition, the analysis of EEG/fMRI data provides a fundamental insight into the precise physiological meaning of both fMRI and EEG data. Routine application of EEG/fMRI for localization of epileptic sources is hampered by large artefacts in the EEG, caused by switching of scanner gradients and heartbeat effects. Residuals of the ballistocardiogram (BCG) artefacts are similarly shaped as epileptic spikes, and may therefore cause false identification of spikes. In this study, new ideas and methods are presented to remove gradient artefacts and to reduce BCG artefacts of different shapes that mutually overlap in time.