Summary Parasitoid acceptance of host individuals that differ in suitability is dynamic, varying with physiological state and experience. Female parasitoids with high egg loads and low life expectancy (i.e. time limited) are more willing to accept hosts with low suitability for progeny development than females with low egg loads and high life expectancy (i.e. egg limited). However, studies of dynamic acceptance behaviour in parasitoids have only considered high‐ vs. low‐suitability host individuals within the same host species. Here, we report the first results on whether acceptance of individuals from different host species that vary in suitability is also dynamic, using two aphid parasitoid species in the genus Aphelinus (Hymenoptera: Aphelinidae). Stressors (starvation and age) and experience that increase time limitation did not affect the acceptance of low‐suitability host species by two Aphelinus species with reciprocal specificities. Oviposition in a high‐suitability host species increased with egg load, but did not vary with egg load for females exposed to low‐suitability host species. This is an unexpected pattern since it results in proportionally higher acceptance of low‐suitability hosts with decreasing egg load. The stability of behavioural host specificity in these parasitoids under very stressful conditions might be explained by (i) frequent transient egg limitation, (ii) higher fitness from egg resorption than oviposition or (iii) neural constraints on host recognition. If neural constraints restrict the ability of these specialists to change their behaviour under stress, we predict that generalist species of Aphelinus should show greater dynamism in acceptance of low‐suitability hosts. We are testing this prediction using Aphelinus species with very broad host ranges.