Neurons in the fly lobula plate integrate motion signals over large regions of visual space in a directionally selective manner. This study is concerned with the details of this integration process. We used a stimulus consisting of a 4 x 4 lattice of locally moving Gabor patches, in which each patch could take any direction independently. We also presented only one patch at a time, or two patches at a time. Across all possible directions of motion, the firing rate response r₁₊₂ to two simultaneously presented patches was well described by r₁₊₂(d₁,d₂)=G x [r₁(d₁)+r₂(d₂)]+S, where r₁ and r₂ are responses to individual patches moving in directions d₁ and d₂, and G~0.81, S~-23. However, this quasi-linear scaling expression failed to account for three main empirical observations: 1) the directional tuning curve for one patch is broader in the presence of another patch moving in the neuron's preferred direction (PD); 2) the vertical compression of this curve is greater when the second patch moves in the anti-preferred direction (AD) as opposed to PD; 3) the ability of the neuronal response to discriminate the direction of a patch is greater when the other patch is moving in the PD as opposed to AD, where this ability is assessed using both information theory and a standard discriminability index. In order to account for these departures from the simple scaling model, we used a normalization model very similar to one used for macaque area MT/V5. This model can qualitatively explain all three departures from the scaling equation described above, suggesting that a gain-control normalization network may be at work within the fly lobula plate.