The present invention relates to the use of 5-hetaryl-4-aminopyrimidines of the formula I and their salts for controlling plant-damaging fungi. The invention also relates to novel 5-hetaryl-4-aminopyrimidines and to crop protection compositions comprising at least one such compound as active component. Het is an optionally substituted 5- or 6-membered aromatic heterocycle which has 1, 2, 3 or 4 heteroatoms selected from the group consisting of nitrogen, oxygen and sulfur as ring members, where the 5- or 6-membered heteroaromatic radical may have 1, 2, 3 or 4 identical or different substituents L, R1, R2 are inter alia hydrogen, C1-C8-alkyl, C3-C8-cycloalkyl, C5-C10-bicycloalkyl, C2-C8-alkenyl, C4-C10-alkadienyl, C3-C6-cycloalkenyl, C2-C8-alkynyl, phenyl, naphthyl or a five- or six-membered saturated, partially unsaturated or aromatic heterocycle which has one, two, three or four heteroatoms from the group consisting of O, N or S as ring members; or together form a ring; R3 is inter alia hydrogen, OH, halogen, cyano, NR31R32, C1-C8-alkyl, C1-C8-alkoxy, C1-C8-alkylthio, C1-C8-alkylsulfinyl, C1-C8-alkylsulfonyl, C2-C8-alkenyl or C2-C8-alkynyl, and R4 is halogen, cyano, hydroxyl, mercapto, N3, C1-C6-alkyl, C2-C8-alkenyl, C2-C8-alkynyl, C1-C6-haloalkyl, C1-C6-alkoxy, C3-C8-alkenyloxy, C3-C8-alkynyloxy, C1-C6-haloalkoxy, C1-C6-alkylthio, C3-C8-alkenylthio, C3-C8-alkinylthio, C1-C6-haloalkylthio, or is a radical of the formula C(═Z)OR41, C(═Z)NR42R43, C(═Z)NR44—NR42R43, C(═Z)R45, CR46R47—OR48, CR46R47—NR42R43, ON(═CR49R50), O—C(═Z)R45, NR42R43a, NR51(C(═Z)R45), NR51(C(═Z)OR41), NR51(C(═Z)—NR42R43), NR52a(N═CR49R50), NR52NR42R43, NR52OR41 or C(═N—X—R45)SR41.