Six population generations (P1, P2, F1, F2, B1 and B2) were used in the study for two crosses of bread wheat (Triticum aestivum L.), the first cross between two varieties (Abu Ghraib * Milan). While the second cross was between (Ibaa 99 * Ala). Six generations for the crosses were cultivated as according to the complete block design(RCBD) with three replicates in Kirkuk province (perdi area), Generational means
were analyzed for the studied quantitative characteristics of the six generations in crossbreeding, and showed the superiority of F2 population over F1 in their performance and for all traits except for the height of the plant and the area of the leaf where the F1 population outperformed F2. while the dominance genetic variation was significant form zero and for all the studied traits in the two crosses except harvest index and the protein percentage, while the narrow sense heritability was lowest for all traits in the two crosses, due to the low values of additive genetic variation, while the narrow sense heritability was lowest for all traits in the two crosses, due to the low values of additive genetic variation, The results of the analysis showed the inadequacy of the model of the three parameters genetic and of all the characteristics studied in crosses, so the six parameters genetic model was used, which showed that the epistatic effects (d) were significant in all traits except the leaf area of the plant and number spikes per plant in the first cross, while it was significant in the weight of 1000 grains and the efficiency yield in the second cross. The epistatic effects (h) were significant for plant height and grains yield. Plant in crosses, area of the leaf, biological yield, harvest index and yield efficiency in first cross number of grains per Spike and protein percentage in second cross, epistatic effect (i) were Significant in some studied traits for the two crosses, the leaf area of the plant, bio-yield, harvest index, protein percentage in first cross, while leaf area and number of spikes per Plant and number of grains per Spike in second cross. And the epistatic effects (j) are significant in the area of the leaf, the grain yield, the protein ratio for hybridization, the height plant in the first cross, area of the leaf of the plant, and the number of grains. Spike and bio- Yield Plant and the harvest index in the second cross, and the epistatic effects of the type (dominance*dominance) (I) occupied the highest importance in inheriting most of the quantitative traits studied and it was a double pattern to reflect their signal, which is an undesirable genetic pattern and selection is required in late generation.