The quality of oil determined by the constituents and proportion of fatty acid components,and the understanding of heredity of fatty acid components are of importance to breeding good quality soybean varieties.Embryo,cytoplasmic and mateal effects and genotype×environment interaction effects for quality traits of soybean [Glycine max (L.) Merrill.] seeds were analyzed using a general genetic model for quantitative traits of seeds with parents,F1 and F2,of 20 crosses from a diallel mating design of five parents planted in the field in 2003 and 2004 in Harbin,China.The interaction effects of palmitic,stearic,and linoleic acid contents were larger than the genetic main effects,while the genetic main effects were equal to interaction effects for linolenic and oleic acid content.Among all kinds of genetic main effects,the embryo effects were the largest for palmitic,stearic,and linoleic acids,while the cytoplasm effects were the largest for oleic and linolenic acids.Among all kinds of interaction effects,the embryo interaction effects were the largest for fatty acids.The sum of additive and additive× environment effects were larger than that of dominance and dominance×environment effects for the linolenic acid content,but not for other quality traits.The general heritabilities were the main parts of heritabilities for palmitic and oleic acid contents,but the interaction was more important for stearic,linoleic,and linolenic acid contents.For the general heritability,mateal and cytoplasm heritabilities were the main components for palmitic,oleic,and linolenic acid contents.It was shown for the interaction heritabilities that the embryo interaction heritabilities were more important for oleic and linolenic acid contents,while the mateal interaction heritabilities were more important for linoleic acid content.Among selection response components,the mateal and cytoplasm general responses and/or interaction responses were more important for palmitic,stearic,oleic,and linoleic acid contents.The main selection response components were from the embryo general response and / or interaction response for linolenic acid content.It suggested that the selection of palmitic,stearic,oleic,and linoleic acid contents in offspring should be in mateal plants,while linolenic acid content should be improved by screening or selecting the single seed in higher generations.