The authors have created new genetic models of common wheat with different types of intergenomic chromosome substitution or translocation that include genetic materials of taxonomically unrelated species (S. сereale, Ag. elongatum, Ag. intermedium, H. marinum) for the introgression of genes that control adaptation and resistance to biotic and abiotic stress factors, along with the studying of homology between chromosomes. For the identification of rye, barley and wheatgrass chromosomes in the genome of common wheat, the authors used the molecular-cytological analysis of lines based on the genomic in situ hybridization and PCR analysis with the use of specific primers. The genetic relations have been studied in terms of the degree of substitution and compensation ability of particular chromosomes. To study the homology and homeology of chromosomes and control the peculiar features of alien chromosome transmission and elimination via gametes, the authors performed an analysis on chromosomes' synapsis and assortment in the offspring of wheat-alien substitution lines. Newly created models were examined to identify and localize the genes or gene alleles in chromosomes of different genomes and homeologous groups, which control such traits as the type of development and heading stage, and resistance to the impact of unfavorable weather conditions (winter-cold tolerance, stem and leaf rust and powdery mildew tolerance).