We used event-related potentials (ERPs) in a crossmodal stimulus-response compatibility paradigm to identify modality-independent aspects of rule processing and cued response facilitation. Participants responded to a lateralized target with the ipsilateral (compatible) or contralateral (incompatible) hand. Cue-target modality and cue-target order were manipulated. The cue preceded the target in half of the trials, and the target preceded the cue in the other half. For half of the participants, a visual cue signalled the response rule to an auditory target, while in other half, an auditory cue signalled the response rule to a visual target. Behavioural results showed a significant cue facilitation effect with response times faster for trials when the cue preceded the target, regardless of cue-target modality. The overall fastest response times were obtained in auditory cue-visual target trials. We performed groupwise independent component analysis of the cortical potentials and identified two modality-independent spatiotemporal patterns related to experimental effects. The first pattern, which resembled the early part of a contingent-negative waveform, was associated with response rule processing, regardless of cue-target presentation order and modality. The second pattern showed amplitude modulations that were dependent on stimulus modality. However, this pattern also correlated with faster response times only when the cue preceded the target and regardless of cue-target modality. Source analysis suggested that the response rule processing pattern originated from the posterior parietal, motor and cingulate regions. The pattern associated with the cue-first facilitation effect originated from cingulate and medial frontal regions. The effects carried by both patterns showed temporal overlap in the interval between the first and second stimulus presentation, but with differences in their relation to response rule processing and behavioural facilitation.