Technical Abstract: Durum wheat (Triticum turgidum L., 2n = 4x = 28; AABB genomes) is a natural hybrid – an allotetraploid between two wild species, Triticum urartu Tumanian (AA genome) and Aegilops speltoides Tausch (BB genome). As shown earlier, even at the allotetraploid level, durum wheat can tolerate chromosomal imbalance such as addition of alien chromosome 1E of a related diploid wheatgrass [Lophopyrum elongatum (Host) Á. Löve, 2n = 2x = 14; EE genome]. Therefore, one way to broaden its genetic base is to add a desirable alien chromosome/chromatin from its diploid wild relatives. We attempted chromosomal engineering with chromosomes of a diploid wheatgrass, Thinopyrum bessarabicum (Savul and Rayss) Á. Löve (2n = 2x = 14; JJ genome). Several advanced hybrids and alien addition lines involving Th. bessarabicum were studied using traditional cytology, multicolor fluorescent genomic in situ hybridization, and molecular markers. Hybrid derivatives varied in chromosome number from the F1 to F8 self-generations and in backcross generations. In advanced generations, we exercised selection against 28-chromosome plants and for 30-chromosome plants that helped recover 14 addition lines in the F8 generation, as indicated by the absence of segregation for 29-chromosome plants. These disomic additions showed regular meiosis with 15 bivalents, 14 of durum wheat and one of Th. bessarabicum. The identity of the added chromosome(s) in these addition lines could not be determined. The addition lines will facilitate further chromosome engineering work on durum wheat and for broadening its genetic base.