This research tests the hypothesis that sequence learning performance in non-human primates will be modulated both by the structure of the sequences to be learned and by the schedule of reward applied during learning. Sequence learning in humans has been extensively explored with serial reaction time (SRT) protocols where learning is revealed by reduced reaction times for stimuli presented in repeating sequences vs. stimuli presented in random series. The SRT protocol has been used to demonstrate that different types of sequential structure may be learned under different awareness conditions. Here, we consider surface and abstract structure of sensorimotor sequences such that sequences ABCBAC and DEFEDF (where A to F correspond to spatial locations on a touch sensitive screen) have different serial order or surface structure, but share the same abstract structure 123213, and are thus considered isomorphic. In four experiments, we manipulated the type of sequential structure to be learned, and the schedule of reward in spatial sequence learning tasks. Both of the two monkeys tested demonstrated significant SRT learning for serial order or surface structure, while they failed to learn and transfer abstract structure. Their learning performance was also modulated by the schedule of reward. These results are in support of our hypothesis and are discussed in the context of existing models of sensorimotor sequence learning.