The response of a neuron in primary visual cortex (V1) to an optimal stimulus in its classical receptive field (CRF) can be reduced by the presence of an orthogonal mask, a phenomenon known as cross-orientation suppression. The presence of a parallel stimulus outside the CRF can have a similar effect, in this case known as surround suppression. We used a novel stimulus to probe the time course of cross-orientation suppression and found that it is very fast, starting even before the response to optimal excitatory stimuli. However, it occurs with some delay after the offset response, considered to be a measure of the earliest excitatory signals that reach the CRF. We also examined the time course of response to a stimulus presented outside the CRF and found that cross-orientation suppression begins substantially earlier than surround suppression measured in the same cells. Together, these findings suggest that cross-orientation suppression is attributable to either direct feedforward signal paths to V1 neurons or a circuit involving fast local interneurons within V1. Feedback from higher cortical areas is implicated in surround suppression, but our results make this an implausible mechanism for cross-orientation suppression. We conclude that suppression from inside and outside the CRF occur through different mechanisms.