The oculomotor system must convert signals representing the target of an intended eye movement into appropriate input to drive the individual extraocular muscles. Neural models propose that this transformation may involve either a decomposition of the intended eye displacement signal into horizontal and vertical components or an implicit process whereby component signals do not predominate until the level of the motor neurons. Thus decomposition models predict that premotor neurons should primarily encode component signals while implicit models predict encoding of off-cardinal optimal directions by premotor neurons. The central mesencephalic reticular formation (cMRF) and paramedian pontine reticular formation (PPRF) are two brain stem regions that likely participate in the development of motor activity since both structures are anatomically connected to nuclei that encode movement goal (superior colliculus) and generate horizontal eye movements (abducens nucleus). We compared cMRF and PPRF neurons and found they had similar relationships to saccade dynamics, latencies, and movement fields. Typically, the direction preference of these premotor neurons was horizontal, suggesting they were related to saccade components. To confirm this supposition, we studied the neurons during a series of oblique saccades that caused "component stretching" and thus allowed the vectorial (overall) saccade velocity to be dissociated from horizontal component velocity. The majority of cMRF and PPRF neurons encoded component velocity across all saccades, supporting decomposition models that suggest horizontal and vertical signals are generated before the level of the motoneurons. However, we also found novel vectorial eye velocity encoding neurons that may have important implications for saccade control.