The output of retinal ganglion cells depends on local and global aspects of the visual scene. The local receptive field is well studied and classically consists of a linear excitatory center and a linear antagonistic surround. The global receptive field contains pools of nonlinear subunits that are distributed widely across the retina. The subunit pools mediate in uncertain ways various nonlinear behaviors of ganglion cells, like temporal-frequency doubling, saccadic suppression, and contrast adaptation. To clarify mechanisms of subunit function, we systematically examined the effect of remote grating patterns on the spike activity of cat X- and Y-type ganglion cells in vivo. We present evidence for two distinct subunit types based on spatiotemporal relationships between response nonlinearities elicited by remote drifting and contrast-reversing gratings. One subunit type is excitatory and activated by gratings of approximately 0.1 cycles per degree, while the other is inhibitory and activated by gratings of approximately 1 cycle per degree. The two subunit pools contribute to a global gain control mechanism that differentially modulates ganglion cell response dynamics, particularly for ON-center cells, where excitatory and inhibitory subunit stimulation respectively makes responses to antipreferred and preferred contrast steps more transient. We show that the excitatory subunits also have a profound influence on spatial tuning, turning cells from lowpass into bandpass filters. Based on difference-of-Gaussians model fits to tuning curves, we attribute the increased bandpass selectivity to changes in center-surround strength and relative phase and not center-surround size. A conceptual model of the extraclassical receptive field that could explain many observed phenomena is discussed.