Spatial visual attention in humans and mammals is severely disrupted after deactivation of specific cortical or subcortical regions. Such dysfunction has frequently been associated with impaired unilateral cortical mechanisms. Alternatively, I propose that essential mechanisms of spatial attention are based on the bilateral competition between subcortical midbrain structures. Consequently, visuospatial hemineglect and hemi-extinction arise from unbalanced bilateral competition. I present a simple mathematical model, based on known connectivity of the cat midbrain, that exemplifies the principle of competition through mutual inter-hemispheric inhibition. The model represents a linear, topographic integration of several cortical and subcortical inputs in the two halves of the feline superior colliculus. Such a system reproduced a variety of neglect symptoms and also explained the paradoxical effects observed in some lesion experiments where the consequences of a primary lesion could be reversed through a secondary lesion in structures of the contralateral hemisphere. The model generated predictions for future experiments.