NEDD8/RUB, as a ubiquitin-like protein, participates in the post-translational modification of protein and requires unique E1, E2, and E3 enzymes to bind to its substrate. The RUB E1 activating enzyme and E2 conjugating enzyme play a significant role in the neddylation. However, it is unknown whether RUB E1 and E2 exist in pepper and what its function is. In this study, a total of three putative RUB E1 and five RUB E2 genes have been identified in the pepper genome. Subsequently, their physical and chemical properties, gene structure, conserved domains and motifs, phylogenetic relationship, and cis-acting elements were analyzed. The structure and conserved domain of RUB E1 and E2 are similar to that of Arabidopsis and tomato. The RUB E1 and E2 genes were randomly distributed on seven chromosomes, and there were two pairs of collinearity between pepper and Arabidopsis and eight pairs of collinearity between pepper and tomato. Phylogenetic analysis reveals that RUB E1 and E2 genes of pepper have a closer relationship with that of tomato, potato, and Nicotiana attenuate. The cis-elements of RUB E1 and E2 genes contained hormone response and stress response. RUB E1 and E2 genes were expressed in at least one tissue and CaRCE1.3 and CaRCE2.1 were exclusively expressed in flowers and anthers. Moreover, the expression of RUB E1 genes (CaECR1, CaAXR1.1, and CaAXR1.2) and RUB E2 genes (CaRCE1.1, CaRCE1.2, and CaRCE2.1) was increased to varying degrees under low-temperature, drought, salt, ABA, and IAA treatments, while CaRCE1.3 and CaRCE2.2 were down-regulated under low-temperature treatment. In addition, these genes were hardly expressed under MeJA treatment. In summary, this study provides a theoretical foundation to explore the role of RUB E1 and E2 in the response of plants to stress.