In invaded regions, the introduced non-native plants Reynoutria japonica and Impatiens glandulifera show little grazing damage, most likely due to the absence of specialized herbivores and the deterrent effect of secondary metabolites on generalist herbivores. The low degree of grazing damage has been explained by the non-mutually exclusive enemy-release and novel weapon hypotheses. We tested assumptions of these hypotheses by conducting a series of preference tests in which leaf samples from R. japonica, I. glandulifera, and the native Urtica dioica were offered to five species of generalist gastropods (the native Arianta arbustorum, Cepaea nemoralis and Fruticicola fruticum, and the non-native invasive Hygromia cinctella and Arion vulgaris). In addition, we determined the C/N-ratio and total phenolic compounds (as a surrogate of secondary metabolites) of the plant species. In the choice experiment with fresh leaf samples, all snail species showed a preference for U. dioica, with the exception of the non-native invasive slug A. vulgaris, which ate leaf tissue from I. gladulifera almost as much as from U. dioica. The snails’ preference of U. dioica was even more pronounced when the fresh weight of leaf material eaten was considered. No-choice tests with either fresh or dead R. japonica leaves showed that most individuals of all species ate small amounts of fresh leaves, but less of dead leaves. In contrast, no-choice tests with either fresh or senescent I. glandulifera leaf tissue showed that individuals of all five gastropod species consumed larger amounts of senescent leaves than fresh leaves, probably because secondary compounds have been broken down or leached or the leaf texture has changed. The low susceptibility of these non-native invasive plants to the gastropods can most likely be explained by a combination of chemical and physical plant characteristics.