The relationship between neural activity in motor cortex and movement is highly debated. Although many studies have examined the spatial tuning (e.g., for direction) of cortical responses, less attention has been paid to the temporal properties of individual neuron responses. We developed a novel task, employing two instructed speeds, that allows meaningful averaging of neural responses across reaches with nearly identical velocity profiles. Doing so preserves fine temporal structure and reveals considerable complexity and heterogeneity of response patterns in primary motor and premotor cortex. Tuning for direction was prominent, but the preferred direction was frequently inconstant with respect to time, instructed-speed, and/or reach distance. Response patterns were often temporally complex and multiphasic, and varied with direction and instructed speed in idiosyncratic ways. A wide variety of patterns was observed, and it was not uncommon for a neuron to exhibit a pattern shared by no other neuron in our dataset. Response patterns of individual neurons rarely, if ever, matched those of individual muscles. Indeed, the set of recorded responses spanned a much higher dimensional space than would be expected for a model in which neural responses relate to a moderate number of factors-dynamic, kinematic, or otherwise. Complex responses may provide a basis-set representing many parameters. Alternately, it may be necessary to discard the notion that responses exist to "represent" movement parameters. It has been argued that complex and heterogeneous responses are expected of a recurrent network that produces temporally patterned outputs, and the present results would seem to support this view.