The Wheat breeding program at Oklahoma State University(OSU) is introduced with reference to genotype by environment interactions and linear regression analyses. Oklahoma is the second largest producer of hard red winter wheat in the US. The breeding porgram is conducted by the wheat breeding personnel of the Agronomy Department in collaboration with plant pathologists, entomologists and biochemists of OSU and wheat geneticists of the US Department of Agriculture. The main-stream breeding procedures are F2 or F3 progeny methods, which are modifications of pedigree and bulk breeding methods. The procedures for source population development,selection practice and field trials are discussed. The major objective of the projict is to develop wheat varieties with supperior yield and yield stability. Drought stress is a serious constraint to wheat crop and frequently causes substantial yield reduction in Okrahoma. Other major obstacles to wheat production are disease and insect damage which include leaf rust, mosaic diseses, septoria and green bug. Research and breeding activities to overcome thesse obstacles are briefly reviewed.Genotype by environment interactions are commonly found and cause serious problems in identifying superior genotype over a wide range of environments in the wheat breeding program. Linear regression analyses and other yield stability parameters are proposed to characterize genotype responses to varying environments. The grain yield data from cultivar trials during 1971-1982 were analyzed by an analysis of variance method and linear regression method. The analysis of varince indicated substantial genotype by environment interactions. The linear regression analyses could adequately explain much of the interaction and provided parameters to compare yield responses of genotypes over environments. Other stability parameters were also estimated and their relationships were discussed. The linear regression analyses revealed that selection toward higher average yield over environments favored genotypes adapted for high yeilding environments.著者は、1981・1982年と1985~1988年の二度にわたり、米国オクラホマ州立大学の大学院に留学し、硬質冬小麦(Hard Red Winter Wheat)の育種プロジェクトの下、修士(Master of Science)と博士号(Ph.D.in Crop Science)を取得した。本稿では、同州の硬質冬小麦育種プロジェクトについて触れるとともに、量的形質の選抜に際して最大の課題の一つである遺伝子型と環境の交互作用と、その交互作用をそれぞれの遺伝子型の環境との反応性によって説明しようとする方法(直線回帰分析)を用いて解析した例を紹介する