Key messageUsing COS markers, the study reveals homeologous relationships between tetraploid Agropyron cristatum and bread wheat to support alien introgression breeding of wheat.AbstractCrested wheatgrass (Agropyron cristatum L. Gaertn.) is a wild relative of wheat that possesses many genes that are potentially useful in wheat improvement. The species comprises a complex of diploid, tetraploid and hexaploid forms. In this study, wheat–A. cristatum chromosome, telosome and translocation lines were used to characterize syntenic relationships between tetraploid A. cristatum and bread wheat. Prior to mapping COS markers, the cytogenetic stock lines were characterized for fertility and by FISH and GISH for karyotype stability. Out of 328 COS markers selected for the study, 279 consistently amplified products in tetraploid A. cristatum, and, out of these, 139 were polymorphic between tetraploid crested wheatgrass and wheat. Sixty-nine markers were found to be suitable for the detection of tetraploid A. cristatum chromosomes 1P–6P in wheat, ranging from 6 to 17 markers per chromosome. BLASTn of the source ESTs resulted in significant hits for 67 markers on the wheat pseudomolecules. Generally, COS markers of the same homeologous group were detected on similar arms in both Agropyron and wheat. However, some intragenomic duplications and chromosome rearrangements were detected in tetraploid A. cristatum. These results provide new insights into the structure and evolution of the tetraploid A. cristatum genome and will facilitate the exploitation of the wild species for introgression breeding of bread wheat.Electronic supplementary materialThe online version of this article (10.1007/s00122-019-03394-1) contains supplementary material, which is available to authorized users.