Pavlovian conditioning is a ubiquitous form of associative learning that enables animals to remember appetitive and aversive experiences. Animals possess appetitive and aversive conditioning systems that memorize and retrieve appetitive and aversive experiences. Here, we addressed a question of whether integration of competing appetitive and aversive information takes place during the encoding of the experience or during memory retrieval. We developed novel experimental procedures to address this question using crickets (Gryllus bimaculatus), which allowed selective blockade of the expression of appetitive and aversive memories by injecting octopamine and dopamine receptor antagonists. We conditioned an odour (conditioned stimulus 1, CS1) with water and then with sodium chloride solution. At 24 h after conditioning, crickets retained both appetitive and aversive memories, and the memories were integrated to produce a conditioned response (CR). Importantly, when a visual pattern (CS2) was conditioned with CS1, appetitive and aversive memories formed simultaneously. This indicates that appetitive and aversive second-order conditionings are achieved at the same time. The memories were integrated for producing a conditioned response. We conclude that appetitive and aversive conditioning systems operate independently to form parallel appetitive and aversive memories, which compete to produce learned behaviour in crickets.