Automatic and postlexical semantic processing in the cerebral hemispheres was studied by presenting categorically related but nonassociated word pairs (e.g., TABLE-BED) to the left visual field (LVF) or to the right visual field (RVF) in semantic priming experiments. Experiment 1 examined automatic priming across stimulus onset asynchronies (SOAs) of 165 and 750 ms with a low proportion of related pairs and a low nonword ratio, employing a GO-NOGO lexical decision task. In contrast to an earlier view that a larger range of meanings is automatically activated in the right than in the left hemisphere, priming was observed in the RVF/left hemisphere only. SOA did not exert any effects. In Experiment 2, postlexical semantic matching of the prime and the target was encouraged by requiring subjects to respond to both of them at the same time. Now there was priming in the LVF, suggesting that a postlexical matching process works in the right hemisphere. The earlier studies showing a right hemisphere advantage in categorical priming are reinterpreted according to the postlexical right hemisphere hypothesis.