Tetraploid species T. dicoccum Shuebl is a potential source of drought tolerance for cultivated wheat, including common wheat. This paper describes the genotyping of nine stable allolines isolated in the offspring from crossing of T. dicoccum x T. aestivum L. using 21 microsatellite (simple sequence repeats—SSR) markers and two cytoplasmic mitochondrial markers to orf256, rps19-p genes; evaluation of drought tolerance of allolines at different stages of ontogenesis (growth parameters, relative water content, quantum efficiency of Photosystem II, electron transport rate, energy dissipated in Photosystem II); and the study of drought tolerance regulator gene Dreb-1 with allele-specific PCR (AS-MARKER) and partial sequence analysis. Most allolines differ in genomic composition and T. dicoccum introgressions. Four allolines—D-b-05, D-d-05, D-d-05b, and D-41-05—revealed signs of drought tolerance of varying degrees. The more drought tolerant D-41-05 line was also characterized by Dreb-B1 allele introgression from T. dicoccum. A number of non-specific patterns and significant differences in allolines in regulation of physiological parameters in drought conditions is identified. Changes in photosynthetic activity in stress-drought are shown to reflect the level of drought tolerance of the forms studied. The contribution of different combinations of nuclear/cytoplasmic genome and alleles of Dreb-1 gene in allolines to the formation of stress tolerance and photosynthetic activity is discussed.