Disclosed are pyrimidine derivatives represented by general formula ##STR1## wherein Z.sup.1 represents an alkynyl group, an alkenyl group, an alkoxy group, an alkenyloxy group, or an alkynyloxy group which may be substituted with a halogen atom, and Z.sup.2 represents a hydrogen atom, a halogen atom, an alkyl group, an alkoxy group, or a group of the formula ##STR2## where Z.sup.3 represents a hydrogen atom or a methyl group; or its salt; and processes for preparing same. Also, agricultural or horticultural compositions containing the pyrimidine derivatives as active ingredient are disclosed, which show high controlling activities for cucumber gray mold (Botrytis cinerea), cucumber downey mildew (Pseudoperonospora cubensis), Alternaria sooty spot of Chinese mustard (Alternaria brassicicola), rice blast (Pyricularia oryzae), etc.