The Asian spotted wing drosophila, Drosophila suzukii, has recently become a serious pest of soft fruits in Europe. Classical biological control through the introduction of larval parasitoids from its native range in Asia is presently being considered. However, host specificity of potential biological control agents has to be determined to avoid releasing species that may have unintended non-target impacts. Larvae of six different European non-target fly species and the target D. suzukii were exposed either on diet or blueberries to three Asian larval parasitoids, Asobara japonica, Leptopilina japonica, and Ganaspis cf. brasiliensis, and one European species, Leptopilina heterotoma. Asobara japonica showed the lowest specificity, attacking and developing in all Drosophilidae. Leptopilina japonica successfully parasitized two non-target Drosophilidae, D. melanogaster and D. subobscura, with one singly progeny emerging from D. immigrans. Ganaspis cf. brasiliensis had the highest level of specificity but variations occurred between two geographical populations tested. A Japanese population was strictly specific to D. suzukii, whereas another population from China parasitized D. suzukii, D. melanogaster and sporadically D. subobscura. The European L. heterotoma successfully developed in D. melanogaster, D. subobscura and occasionally in D. immigrans, but nearly all eggs and larvae in D. suzukii were encapsulated. These results show that Ganaspis cf. brasiliensis is the species with the highest potential for biological control, but more studies are needed on its taxonomic status and the existence of biotypes or cryptic species varying in their specificity before field releases can be conducted in Europe.Electronic supplementary materialThe online version of this article (10.1007/s10340-018-1003-z) contains supplementary material, which is available to authorized users.