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Many plants can avoid the adverse effects of drought by developing special epidermal cell bladders which may serve as external water reservoirs and having small and thick-walled cells. The present investigation aimed at: (i) studying the effect of drought stress on quinoa leaf anatomical traits and their heritability, genetic advance from selection and (ii) describing differences among drought tolerant and susceptible genotypes in such traits following the imposition of water deficit. A field experiment was carried out in the growing season 2015/2016, using a split plot design with five replications. Main plots were allotted to three irrigation regimes, i.e. well watering (WW) [95% field capacity (FC)], moderate water stress (WS) [65% FC] and severe water stress (SWS) [35% FC] and sub plots to five genotypes. Mean squares due to genotypes, irrigation regimes and their interaction were significant for all studied leaf anatomical traits. Water stress caused a significant decrease in leaf thickness under WS and SWS, upper and lower epidermis under WS, palisade and spongy layers under SWS, but caused a significant increase in palisade and spongy layers under WS and upper and lower epidermis under SWS. The genotype CICA-17 (tolerant genotype) was the first in thickness for upper epidermis, and leaf and second in lower epidermis, palisade and spongy layers. On the other hand, the genotypes Ollague (sensitive) had the thinnest layers in upper and lower epidermis. Broad-sense heritability estimates for anatomical traits were very high in magnitude (>87.0%), except for lower epidermis (41.18, 59.41 and 33.33%) under WW, WS and SWS, respectively. Genetic advance from selection ranged from 15.40% for upper epidermis to 72.97% for palisade layer under SWS, from 52.66% for leaf thickness to 82.72% for palisade layer under WS and from 30.40% for leaf thickness to 87.12% for spongy layer under WW.