We studied neurons in areas V1, V2, and posteromedial lateral suprasylvian area (PMLS) of anesthetized cats, assessing their speed tuning using steps to constant speeds and acceleration and deceleration tuning using speed ramps. The results show that the speed tuning of neurons in all three cortical areas is highly dependent on prior motion history, with early responses during speed steps tuned to higher speeds than later responses. The responses to speed ramps are profoundly influenced by speed-dependent response latencies and ongoing changes in neuronal speed tuning due to adaptation. Acceleration evokes larger transient and sustained responses than subsequent deceleration of the same rate with this disparity increasing with ramp rate. Consequently, there was little correlation between preferred speeds measured using speed steps, acceleration or deceleration. From 146 recorded cells, the proportion of cells that were clearly speed tuned ranged from 69 to 100% across the three brain areas. However, only 13 cells showed good skewed Gaussian fits and systematic variation in their responses to a range of accelerations. Although suggestive of acceleration coding, this apparent tuning was attributable to a cell's speed tuning and the different stimulus durations at each acceleration rate. Thus while the majority of cells showed speed tuning, none unequivocally showed acceleration tuning. The results are largely consistent with an existing model that predicts responses to accelerating stimuli developed for macaque MT, which showed that the responses to acceleration can be decoded if adaptation is taken into account. However, the present results suggest future models should include stimulus-specific adaptation and speed-dependent response latencies.