Ternary pesticidal mixtures comprising, as active components, an anthranilamid compound of the formula I wherein the variables are defined according to the description, and two fungicidal compounds II and III selected from the following groups: azoles, strobilurins, carboxamides, heterocylic compounds, carbamates, guanidines, antibiotics, nitrophenyl derivates, sulfur-containing heterocyclyl compounds, organometal compounds and other active compounds according to the description, in a synergistically effective amount, methods for controlling pests, and harmful fungi, methods of protecting plants from attack or infestation by insects, acarids or nematodes, methods for treating, controlling, preventing or protecting an animal against infestation or infection by parasites, compositions containing these mixtures, and methods for their preparation.