Earlier research has shown that speakers naming object pairs can retrieve their names in parallel, but often fail to do so. The conditions for the occurrence of parallel object processing are largely unknown. We examined how associations between objects affected the speakers’ processing strategies. In Experiment 1, participants named object triplets in a left-right-bottom order. During the saccade towards the right object (interloper), it was replaced by a new object (target). We varied the relationship between interloper and target (conceptually related or unrelated) and between interloper and left object (categorically related, associated, unrelated). Target gaze durations were shorter after related than unrelated interlopers. However, this preview effect was independent of the interloper-left object relationship, suggesting that the left and right object were processed sequentially. In Experiments 2 and 3, participants named pairs of associated or unrelated objects. The left objects were repeated several times in each test block to facilitate their processing. Gaze durations for the left objects were longer in associated than unrelated pairs, consistent with parallel processing of the associated objects and interference among them. We will discuss how the difficulty of processing the objects and the relationship between them jointly determine speakers’ processing strategy.