This study used eight genetic structures of Linum Usitatissimum L. (Sakha1, Sakha2, Sakha3, Sakha5, Sakha6, Giza, Syrian and Poloni) and their half-exchange satire obtained according to the second method proposed by Griffing (1956). Genetic compositions (8 parents + 28 hybrids) were planted in the fields of the Faculty of Agriculture/University of Kirkuk in the winter season (2021-2022) by full random sectors (RCBD) with three repeats to study studied qualities (Plant rise, number of days of flowers, 50%, number of days of Knot, 50%, number of days of physiological maturity, number of branches, number of capsules, number of capsule seeds, weight of 1000 seeds, biological product, seed product and harvest guide) by assessing the combining public and private capacities. The results can be summarized as the majority of parents and second-generation hybrids differ morally in all the characteristics studied at a probability level (1%) And (5%), the ratio between the components of the variation of the general combining capacity to the components of the variation of the special combining capacity was less than the correct one for the qualities of the number of flowers days, the knot, the number of capsules, the number of capsule seeds, the harvest guide, the height of the plant, the number of branches, the weight of 1,000 seeds, the biological product, the number of ripening days, the seed and the height of the plant (cm), the number of branches and biological quotient, and the best father (Giza 8) was found to have a general combining ability in qualifications the number of days of the knot, the number of capsules, the seed crop and the biological crop. The hybrid (Sakha 5 * Sakha 2) gave the combining special ability to characterize the plant’s height, number of days flowering, knot, maturity, number of branches, weight of 1000 seed, number of capsules and biological product, Dominance variation values were greater than additional variation values in all qualities except the number of capsules and the seed crop, and inheritance values in the broad sense were found to be high for all the qualities studied except the number of flowering days and the number of capsules that were medium, inheritance in a narrow sense was slow for all the characteristics studied except those of the number of capsules and the weight of 1,000 seeds and the seed crop was medium, the degree rate of dominance was greater than the right one for all the characteristics studied, because the dominance genetic verb is the controller of these qualities. The projected genetic improvement values as a percentage were low for all studied qualities.