In bilateral rapid serial visual presentation (RSVP), the second of two targets, T1 and T2, is better identified in the left visual field (LVF) than in the right visual field (RVF). This LVF advantage may reflect hemispheric asymmetry in temporal attention or/and in spatial orienting of attention. Participants performed two tasks: the "standard" bilateral RSVP task (Exp.1) and its unilateral variant (Exp.1 & 2). In the bilateral task, spatial location was uncertain, thus target identification involved stimulus-driven spatial orienting. In the unilateral task, the targets were presented block-wise in the LVF or RVF only, such that no spatial orienting was needed for target identification. Temporal attention was manipulated in both tasks by varying the T1-T2 lag. The results showed that the LVF advantage disappeared when involvement of stimulus-driven spatial orienting was eliminated, whereas the manipulation of temporal attention had no effect on the asymmetry. In conclusion, the results do not support the hypothesis of hemispheric asymmetry in temporal attention, and provide further evidence that the LVF advantage reflects right hemisphere predominance in stimulus-driven orienting of spatial attention. These conclusions fit evidence that temporal attention is implemented by bilateral parietal areas and spatial attention by the right-lateralized ventral frontoparietal network.