Three populations of common bread wheat (Triticum aestivum L. em. Thell.) were studied to gain an estimate of the genetic variability associated with four agronomic characters in each population. The primary objective was to determine if homozygous lines could be isolated from these populations that would be equal to or better than the F1 of the respective population. Two populations (population 1 and 3) exhibited heterosis for yield in the F1 generation while the other population (population 2) showed no heterosis for yield in the F1. Each population consisted of random F4 lines, each of which could be traced to a single F2 plant. Population 1 originated from a cross of the cultivars \u27Seneca\u27 x \u27Knox 62\u27; population 2 from a cross of \u27Monon\u27 x \u27Triumph\u27; and population 3 from a cross of \u27Tenn. 9\u27 x \u27Knox 62\u27. The characters studied were: (1) mature plant height (centimeters), (2) heading date (days past March 31), (3) yield (grams per plot), and (4) kernel weight (grams per 1000 kernels). The experimental design was a randomized com-plete block with two replications and the experiment was grown at three locations. Estimates of broad sense heritability were obtained via variance component analyses. These heritability estimates were used to calculate expected advance through selection for each character in each population. Phenotypic and genotypic correlation coefficients for all characters in all combinations were calculated. Coefficients of variation and genetic coefficients of variation were also computed. Analyses of the data revealed that the non-heterotic population (population 2) had significant (P. = .05) variability for all four characters. Population 1 showed significant (P. = .05) variability for heading date and kernel weight only, and population 3, for only heading date and mature plant height. Heading date in population 3, mature plant height and kernel weight in population 2 were the only characters whose expected F5 means would be better than the best parent. Evidence was found to support a two major gene hypothesis for the inheritance of heading time. From the results of this study, it appears that homozygous lines that equal or better the F1 could not be found in later generations