The right hemisphere has been shown to play a dominant role in processing of visuo-spatial information. Recently, this role has been studied in the two-stream rapid serial visual presentation task. In this task, two alphanumerical targets are embedded in left and right simultaneous streams of rapidly changing letters. The second target (T2) is identified better in the left than in the right visual field. This difference has been interpreted as advantage of the right hemisphere (RH). However, a disadvantage of the left hemisphere (LH) could not be excluded so far. The LH, specialized for processing of verbal stimuli, might be overloaded due to constant input of letters from both visual fields. In the present study, this overload hypothesis was tested by reducing demands on verbal processing (Experiment 1), and by overloading the RH with non-verbal stimuli: faces (Experiment 2) and irregular shapes (Experiment 3). The left visual field advantage proved to be largely independent from the level of verbal load and from stimulus type. Therefore, although not entirely disproving the overload hypothesis, these results suggest as the most parsimonious explanation this asymmetry reflects a RH advantage, presumably in perceptual and attentional processing, rather than a LH disadvantage caused by verbal overload.