The neural basis of the blood oxygenation level-dependent (BOLD) response measured using fMRI is poorly understood. This work involves a parallel study using fMRI and MEG to explore the relationship between the neuromagnetic and the BOLD responses in motor cortex. Linearity of the BOLD response was investigated using a simple graded motor task, manipulating stimulus duration. Significant changes in the BOLD response, and β-band synchrony were localised to the contra-lateral primary motor cortex, with the appearance of ipsilateral activation on lowering the statistical threshold. This suggests a strong correlation between the two responses. The BOLD time-courses were compared with virtual sensor traces at the peak of β-band activity. Linearity of the event-related desynchronisation (ERD) in the β-band response during movement and the corresponding post-movement β-rebound were investigated. The BOLD responses were found to increase monotonically and non-linearly with stimulus duration, whereas the β-band ERD produced a roughly linear increase. The non-linearity in BOLD is probably largely haemodynamic in origin, but it could also reflect other neural phenomena, including the β-rebound.