We examined the generality of the claim that stereoscopic disparity is detectable in parallel across the visual field. Using a search paradigm with random-dot stereograms, we varied the relative disparity of target and distractor items. When both target and distracters had crossed disparities, both search functions (i.e., target in front of distracters and target behind distracters) were linear with positive slopes. When both target and distracters had uncrossed disparities, the pattern of results depended upon whether the target was in front of or behind the distractors-specifically, when the target was in front of the distracters, search functions were similar to those seen for ''crossed'' search, but when the target was behind the distracters, a nonlinear search function was found. Finally, when the target and distracters straddled the plane of fixation, a nonlinear search function was found when the target was in front of the distracters; however, when the target was behind the distracters, a linear search function with a large positive slope was found. Ne show that the nonlinear search functions are consistent with the effects of an intervening global surface percept. We also show that the size of the stimulus display may be a factor in some relative depth cases. Additionally, we replicate Steinman's (1987) finding that search is parallel when the distracters are located at the plane of fixation and the target disparity is crossed, eliminating monocular and spatial cues to target presence that may have been present in his original study. in a final control experiment, we showed that reaction times did not increase with set size when observers performed another kind of perceptual task on similar random-dot stereogram displays. This eliminates the possibility that some of the results obtained here can be explained by increases in the difficulty of perceiving/fusing the stimuli when the number of distracters is increased.