Sequence learning is common to all motor systems and is an essential aspect of human behavior necessary for the acquisition of motor skill. Many previous studies have demonstrated the ability to observe, store, and repeat sequences in a variety of modalities resulting in reduced reaction time. Recently, it has been found that subjects can make predictive smooth eye movements to a sequence of discrete horizontal target motions (C. J. Collins & Barnes, 2005). The present study extends that paradigm into two dimensions of motion in order to investigate qualitative and quantitative differences in sequences of vertical (V) and horizontal (H) eye movements. The subjects performed sequences of four discrete velocity ramps repeated either four or eight times in succession. Baseline measurements were obtained to discrete individual smooth pursuit velocity ramps to H and V predictable (PRD) and randomized (RND) targets. We found that subjects could rapidly learn and anticipate individual components of a four-ramp sequence in two dimensions. The results showed clear asymmetries in the eye movements made to horizontal and vertical targets. We found that the latencies to H targets were shorter than latencies to V targets in both the PRD and RND conditions. We also found higher initial eye velocity (50 ms after target onset) to H targets than vertical targets during the PRD condition. Because these differences in H and V eye movements are present in both RND and PRD trials, this suggests that the observed differences are not due to retention of information but are inherent asymmetries within the system.