Beneficial insects, such as natural enemies, are important to agro‐ecosystem functioning and thus agricultural production. Parasitoids and predators can provide sustainable long‐term solutions to pest problems (biological control), reducing the need for expensive and sometimes polluting pesticide applications. When several species of beneficial insects are present, their pest control actions may be additive, synergistic, or disruptive. One form of disruptive interaction between parasitoids and predators is direct interspecific contest for access to individual pests (the resource to be exploited). This study evaluated behavioural interactions between brood‐guarding wasps, Goniozus nephantidis (Muesebeck) (Hymenoptera: Bethylidae), which are known to engage in intra‐specific contests, and a predatory bug, Cardiastethus exiguus (Poppius) (Hemiptera: Anthocoridae), which attack the same pest species, Opisina arenosella (Walker) (Lepidoptera: Oecophoridae), a major pest in coconut production systems. Dyadic parasitoid–predator and predator–predator contests were staged to determine the factors that influence the behaviours within, and outcomes of, such interactions. Parasitoids were aggressive towards predators, sometimes killing them, but predators were not aggressive towards parasitoids. Biting and stinging only occurred when there was a host larva present. In the absence of the parasitoid that had oviposited onto a host, predators often consumed the parasitoid’s eggs. Egg consumption sometimes occurred when the parasitoid was present. Intra‐specific competition between pairs of predators was also evaluated: adults were aggressive towards each other, but interactions were not fatal. Biting was more common when there was no prey larva present. When a larva was present, predators were observed feeding simultaneously. We conclude that direct parasitoid–predator interactions are likely to influence pest population dynamics, possibly reducing the overall suppression of O. arenosella by its natural enemies.