In somatosensory cortex, tactile stimulation within the neuronal receptive field (RF) typically evokes a transient excitatory response with or without postexcitatory inhibition. Here, we describe neuronal responses in which stimulation on the hand is followed by suppression of the ongoing discharge. With the use of 16-channel microelectrode arrays implanted in the hand representation of primary somatosensory cortex of New World monkeys and prosimian galagos, we recorded neuronal responses from single units and neuron clusters. In 66% of our sample, neuron activity tended to display suppression of firing when regions of skin outside of the excitatory RF were stimulated. In a small proportion of neurons, single-site indentations suppressed firing without initial increases in response to any of the tested sites on the hand. Latencies of suppressive responses to skin indentation (usually 12-34 ms) were similar to excitatory response latencies. The duration of inhibition varied across neurons. Although most observations were from anesthetized animals, we also found similar neuron response properties in one awake galago. Notably, suppression of ongoing neuronal activity did not require conditioning stimuli or multi-site stimulation. The suppressive effects were generally seen following single-site skin indentations outside of the neuron’s minimal RF and typically on different digits and palm pads, which have not often been studied in this context. Overall, the characteristics of widespread suppressive or inhibitory response properties with and without initial facilitative or excitatory responses add to the growing evidence that neurons in primary somatosensory cortex provide essential processing for integrating sensory stimulation from across the hand. © 2016 the American Physiological Society.