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Background Sesame is an important oilseed crop mainly grown in inclement areas with high temperatures and frequent drought. Thus, drought constitutes one of the major constraints of its production. The AP2/ERF is a large family of transcription factors known to play significant roles in various plant processes including biotic and abiotic stress responses. Despite their importance, little is known about sesame AP2/ERF genes. This constitutes a limitation for drought-tolerance candidate genes discovery and breeding for tolerance to water deficit. Results One hundred thirty-two AP2/ERF genes were identified in the sesame genome. Based on the number of domains, conserved motifs, genes structure and phylogenetic analysis including 5 relatives species, they were classified into 24 AP2, 41 DREB, 61 ERF, 4 RAV and 2 Soloist. The number of sesame AP2/ERF genes was relatively few compared to that of other relatives, probably due to gene loss in ERF and DREB subfamilies during evolutionary process. In general, the AP2/ERF genes were expressed differently in different tissues but exhibited the highest expression levels in the root. Mostly all DREB genes were responsive to drought stress. Regulation by drought is not specific to one DREB group but depends on the genes and the group A6 and A1 appeared to be more actively expressed to cope with drought. Conclusions This study provides insights into the classification, evolution and basic functional analysis of AP2/ERF genes in sesame which revealed their putative involvement in multiple tissue-/developmental stages. Out of 20 genes which were significantly up- /down-regulated under drought stress, the gene AP2si16 may be considered as potential candidate gene for further functional validation as well for utilization in sesame improvement programs for drought stress tolerance. Electronic supplementary material The online version of this article (doi:10.1186/s12870-016-0859-4) contains supplementary material, which is available to authorized users.