NOVELTY - Pyrimidine compounds (I) are new.    USE - (I) are useful for combating animal pests (claimed), which are arthropods, preferably insects, arachnids, helminths and nematodes in agriculture, horticulture, animal husbandry, forests, gardens and hygiene sector. (I) are useful as herbicides, safeners, growth regulators, fungicides, antimycotics, bactericides, virucide, an agent to combat Mycoplasma-like organism and Rickettsia-like organism, and an intermediate for the synthesis of other substances. (I) are useful for protecting seed of maize, peanut, cotton, sugar beet, rice, millet, wheat, barley, oats, sunflower, tobacco and potatoes. The ability of (I) to combat Lucilia cuprina was tested in horse meat. The result showed that N-(4-cyclopropylamino-6-(3,4-difluoro-phenyl)-pyrimidin-5-yl)-2-ethyl-nicotinamide at a concentration of 100 ppm exhibited a pesticidal effect of greater than or equal to 80%.    ADVANTAGE - (I) provide crop with high yield, quality, tolerance to high or low temperatures, dry, water or salinity, high flowering rate, nutritional value and storage stability. (I) exhibit low warm blood toxicity. (I) are eco-friendly and safe to use. (I) in combination with other drugs e.g. insecticides, sterilizing agents, bactericides, acaricides and nematicides exhibit high synergistic effect to combat insects, arachnids, helminths and nematodes.    DETAILED DESCRIPTION - Pyrimidine compounds of formula (I) are new.    R1 = phenyl, naphthyl, phenylalkyl, heteroaryl, heteroarylalkyl, heterocyclyl or heterocyclylalkyl (all optionally substituted), H, alkyl, alkenyl, alkynyl, haloalkyl, cyanoalkyl, cycloalkyl, halocycloalkyl, cycloalkenyl, halocycloalkenyl, hydroxyalkyl, alkoxyalkyl, haloalkoxyalkyl, alkoxyhaloalkyl, alkylcarbonylalkyl, alkoxycarbonylalkyl, alkylsulfanylalkyl, alkylsulfinylalkyl, alkylsulfonylalkyl, haloalkylsulfanylalkyl, haloalkylsulfinylalkyl, haloalkylsulfonylalkyl, halocycloalkylalkyl or cycloalkylalkyl;    R2 = phenyl, naphthyl, phenylalkyl, heteroaryl, heteroarylalkyl, heterocyclyl or heterocyclylalkyl (all optionally substituted), H, alkyl, alkenyl, alkynyl, haloalkyl, cyanoalkyl, cycloalkyl, halocycloalkyl, cycloalkenyl, halocycloalkenyl, hydroxyalkyl, alkoxyalkyl, haloalkoxyalkyl, alkoxyhaloalkyl, alkylcarbonylalkyl, alkoxycarbonylalkyl, alkylsulfanylalkyl, alkylsulfinylalkyl, alkylsulfonylalkyl, haloalkylsulfanylalkyl, haloalkylsulfinylalkyl, haloalkylsulfonylalkyl or cycloalkylalkyl;    R3 = phenyl, naphthyl, phenylalkyl, heteroaryl, heteroarylalkyl, heterocyclyl or heterocyclylalkyl (all optionally substituted), H, alkyl, alkenyl, alkynyl, haloalkyl, cyanoalkyl, cycloalkyl, halocycloalkyl, cycloalkenyl, halocycloalkenyl, hydroxyalkyl, alkoxyalkyl, alkylthioalkyl, haloalkoxyalkyl, alkoxyhaloalkyl, alkylcarbonylalkyl, alkoxycarbonylalkyl, alkylsulfanylalkyl, alkylsulfinylalkyl, alkylsulfonylalkyl, haloalkylsulfanylalkyl, haloalkylsulfinylalkyl, haloalkylsulfonylalkyl or cycloalkylalkyl;    R4 = phenyl, naphthyl, heteroaryl, heteroarylalkyl, heterocyclyl or heterocyclylalkyl (all optionally substituted);    R5 = alkyl, cycloalkyl, phenyl, naphthyl, heteroaryl, heteroarylalkyl, heterocyclyl or heterocyclylalkyl (all optionally substituted), H, halo or CN;    R6 = phenyl, naphthyl, phenylalkyl, heterocyclylalkyl, heteroarylalkyl or phenylcarbonyl (all optionally substituted), H, halo, alkyl, haloalkyl, cyanoalkyl, alkoxyalkyl, alkylcarbonyl, haloalkylcarbonyl, cycloalkyl, halocycloalkyl, cycloalkylalkyl, alkylsulfonyl, alkenyl, alkynyl, alkoxycarbonyl, alkenyloxycarbonyl, alkynyloxycarbonyl or alkoxycarbonylalkyl; and    X = O or S.    An INDEPENDENT CLAIM is included for an agent comprising (I), diluting agent and/or surface active substances.