Heterocyclically substituted anilinopyrimidines of the formula (I) in which R1 to R10 and L1, L2, E1, E2, E3, Y and Z have the meanings given in the description, and agrochemically active salts thereof, their use and also methods and compositions for controlling phytopathogenic harmful fungi in and/or on plants or in and/or on seed of plants, processes for preparing such compositions and treated seed and also their use for controlling phytopathogenic harmful fungi in agriculture, horticulture and forestry, in the protection of materials and in the domestic and hygiene field. The present invention furthermore relates to a process for preparing heterocyclically substituted anilinopyrimidinenes of the formula (I).