Area V2 is a major visual processing stage in mammalian visual cortex, but little is currently known about how V2 encodes information during natural vision. To determine how V2 represents natural images, we used a novel nonlinear system identification approach to obtain quantitative estimates of spatial tuning across a large sample of V2 neurons. We compared these tuning estimates with those obtained in area V1, in which the neural code is relatively well understood. We find two subpopulations of neurons in V2. Approximately one-half of the V2 neurons have tuning that is similar to V1. The other half of the V2 neurons are selective for complex features such as those that occur in natural scenes. These neurons are distinguished from V1 neurons mainly by the presence of stronger suppressive tuning. Selectivity in these neurons therefore reflects a balance between excitatory and suppressive tuning for specific features. These results provide a new perspective on how complex shape selectivity arises, emphasizing the role of suppressive tuning in determining stimulus selectivity in higher visual cortex.