Ternary pesticidal mixtures comprising, as active components, an anthranilamide compound of the formula I which is selected from 3-bromo-4-cyano-1-(3-chloro-2-pyridyl)-2-methyl-6-(methylcarb¬amoyl)pyra¬zole-5-carboxanilide, and 3-bromo-4-chloro-1-(3-chloro-2-pyridyl)-2-methyl-6-(methylcarb¬amoyl)pyrazole-5-carboxanilide and one fungicidal compound II selected from the group of strobilurins, and one fungicidal compound III which is thiophanate-methyl 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.