The ecological impact of an invasive species can be heterogeneous through space and time. One such case in Australia involves native freshwater crocodiles Crocodylus johnstoni, which are highly sensitive to invasive cane toads Rhinella marina in some areas, whereas other populations experience little or no mortality from ingestion of the toxic toads. We studied the impact of toad invasion on three crocodile populations: one crashed, one showed a minor decrease and one appeared unaffected. We tested three hypotheses for the cause of this spatial variation in impact: differences among populations in toad–crocodile encounter rates (proximity of toads to crocodiles during spotlight surveys), differences in crocodile feeding responses (trials of prey preference in the laboratory) and differences in crocodile physiology (reduction of swim speed after receiving a dose of toad toxin). We found little divergence among populations in any of these traits: crocodiles from the three populations all encountered cane toads in the wild, and exhibited similar feeding responses and toxin tolerances. Thus, we cannot confidently identify causation for the impact heterogeneity. Reliance on alternative food resources and an ability to rapidly learn taste aversion may have allowed crocodiles to deal with toad arrival in Lake Argyle and the Daly River. Future work could usefully evaluate potential explanations for the failure of these adaptive mechanisms in the severely affected (Victoria River) population. We suggest that spatial variation in the availability of alternative prey (and thus the willingness of crocodiles to attack a novel toxic prey item) may have contributed to that variation in impact.