Diploid species of the genus Triticum L. are its most ancient representatives and have the A genome, which was more recently inherited by all polyploid species. Studies of the phylogenetic relationships among diploid and polyploid wheat species help to identify the donors of elementary genomes and to examine the species specificity of genomes. In this study, molecular analysis of the variable sequences of three nuclear genes (Acc-1, Pgk-1, and Vrn-1) was performed for wild and cultivated wheat species, including both diploids and polyploids. Based on the sequence variations found in the genes, clear differences were observed among elementary genomes, but almost no polymorphism was detected within each genome in polyploids. At the same time, the regions of the three genes proved to be rather heterogeneous in the diploid species Triticum boeoticum Boiss., T. urartu Thum. ex Gandil., and T. monococcum L., thus representing mixed populations. A genome variant identical to the A genome of polyploid species was observed only in T. urartu. Species-specific molecular markers discriminating the diploid species were not found. Analysis of the inheritance of morphological characters also failed to identify a species-specific character for the three diploid wheat species apart from the hairy leaf blade type, described previously.