Directing attention to one of two superimposing surfaces composed of dot fields rotating in opposing directions facilitates processing of brief translations of the attended surface [Valdes-Sosa, M., Bobes, M. A., Rodriguez, V., & Pinilla, T. (1998). Switching attention without shifting the spotlight object-based attentional modulation of brain potentials. Journal of Cognition and Neuroscience, 10(1), 137–151]. Here we used ERP recordings to investigate the mechanisms of endogenous attentional selection of such competing dot surfaces under conditions of dichoptic viewing (one surface to each eye) and monocular viewing (both surfaces to one eye). Under dichoptic conditions, which induced binocular rivalry, translations of the attended surface presented to one eye elicited enhanced visual P1 and N1 ERP components relative to translations of the unattended surface presented to the other eye. In comparison, during monocular viewing the attended surface translations elicited a significantly larger N1 component in the absence of any P1 modulation. These results indicate that processing of the attended surface is biased at an earlier level in extrastriate visual cortex under conditions of inter-ocular versus intra-ocular competition.