NAC (NAM, ATAF1/2, and CUC2) proteins play a pivotal role in modulating plant development and offer protection against biotic and abiotic stresses. Until now, no systematic knowledge of NAC family genes is available for the food security crop, sweet potato. Here, a comprehensive genome-wide survey of NAC domain-containing proteins identified 130 ItbNAC and 144 ItfNAC genes with full length sequences in the genomes of two diploid wild relatives of cultivated sweet potato, Ipomoea triloba and Ipomoea trifida, respectively. These genes were physically mapped onto 15 I. triloba and 16 I. trifida chromosomes, respectively. Phylogenetic analysis divided all 274 NAC proteins into 20 subgroups together with NAC transcription factors (TFs) from Arabidopsis. There were 9 and 15 tandem duplication events in the I. triloba and I. trifida genomes, respectively, indicating an important role of tandem duplication in sweet potato gene expansion and evolution. Moreover, synteny analysis suggested that most NAC genes in the two diploid sweet potato species had a similar origin and evolutionary process. Gene expression patterns based on RNA-Seq data in different tissues and in response to various hormone, biotic or abiotic treatments revealed their possible involvement in organ development and response to various biotic/abiotic stresses. The expression of 36 NAC TFs, which were upregulated in the five tissues and in response to mannitol treatment, was also determined by real-time quantitative polymerase chain reaction (RT-qPCR) in hexaploid cultivated sweet potato exposed to drought stress. Those results largely corroborated the expression profile of mannitol treatment uncovered by the RNA-Seq data. Some significantly up-regulated genes related to drought stress, such as ItbNAC110, ItbNAC114, ItfNAC15, ItfNAC28, and especially ItfNAC62, which had a conservative spatial conformation with a closely related paralogous gene, ANAC019, may be potential candidate genes for a sweet potato drought tolerance breeding program. This analysis provides comprehensive and systematic information about NAC family genes in two diploid wild relatives of cultivated sweet potato, and will provide a blueprint for their functional characterization and exploitation to improve the tolerance of sweet potato to abiotic stresses.