There have been several studies on the role of circadian clocks in the regulation of associative learning and memory processes in both vertebrate and invertebrate species. The results have been quite variable and at present it is unclear to what extent the variability observed reflects species differences or differences in methodology. Previous results have shown that following differential classical conditioning in the cockroach, Rhyparobia maderae, in an olfactory discrimination task, formation of the short-term and long-term memory is under strict circadian control. In contrast, there appeared to be no circadian regulation of the ability to recall established memories. In the present study, we show that following operant conditioning of the same species in a very similar olfactory discrimination task, there is no impact of the circadian system on either short-term or long-term memory formation. On the other hand, ability to recall established memories is strongly tied to the circadian phase of training. On the basis of these data and those previously reported for phylogenetically diverse species, it is suggested that there may be fundamental differences in the way the circadian system regulates learning and memory in classical and operant conditioning.