Spatial summation has been studied in simple cells of the cat's visual cortex by examining the responses of pairs of lines. One line was placed in an ON region of the receptive field; the other was placed in an OFF region. When the luminances of the lines were modulated in anti-phase, the excitatory responses to the individual lines were almost synchronous. A simple cell's overt response to the composite stimulus was usually greater than the sum of the overt responses to the two components. The result could be explained by supposing that the underlying response was the linear sum of the excitatory signals but that an overt response occurred only when the underlying response exceeded a fixed threshold value. This was true even of simple cells which exhibited non-linearities of spatial summation, as judged from the waveforms of their responses to moving sinusoidal gratings. When the two lines were modulated in phase, the excitatory responses occurred in different halves of the temporal cycle. Some cells summed antagonistic signals linearly. The waveforms of their responses to moving sinusoidal gratings also implied linear spatial summation. However, other cells whose responses to moving gratings implied linearity of summation did not, in fact, sum antagonistic signals linearly. The excitatory responses evoked in a receptive field region were weaker than the inhibitory responses that could be evoked in the same region. The remaining cells did not sum antagonistic signals linearly. There was imperfect cancellation, resulting in the generation of ON-OFF response components. The excitatory responses evoked in a receptive field region were stronger than the inhibitory responses that could be evoked in the same region. These cells gave responses to sinusoidal gratings that did imply nonlinear spatial summation.