Learning sequential structures is of fundamental importance for a wide variety of human skills. While it has long been debated whether implicit sequence learning is perceptual or response-based, here we propose an alternative framework that cuts across this dichotomy and assumes that sequence learning rests on associative changes that can occur concurrently in distinct processing systems and support the parallel acquisition of multiple uncorrelated sequences. In three experiments we used a serial search task to test critical predictions of this framework. Experiments 1 and 2 showed that participants learnt uncorrelated sequences of auditory letters and manual responses, as well as sequences of visual letters, spatial locations, and manual responses simultaneously, as indicated by a reliable response time (RT) cost incurred by occasional deviants violating either of the sequences. This RT cost was reliable even when participants showing explicit knowledge were excluded. In Experiment 3 learning of spatial and nonspatial sequences was functionally dissociated: whereas a spatio-motor distractor task disrupted learning of location but not of letter sequences, a phonological distractor task had the reverse effect. The distractor tasks thus did not reduce unspecific attentional resources, but selectively disrupted the formation of sequential associations within spatial and nonspatial processing dimensions. These results support the view that implicit sequence learning rests on experience-dependent changes that can occur in parallel in multiple processing systems involved in spatial attention, object recognition, phonological processing, and manual response selection. The resulting dimension-specific sequence representations support independent predictions of what will appear next, where it will appear, and how one will have to respond to it.