Two new deep-water species of the snapping shrimp genus Alpheus Fabricius, 1798 are described based on the material collected by the expeditions BIOPAPUA, BOA1 and MIRIKY, organised by the Muséum National d'Histoire Naturelle in Paris. Alpheus alaincrosnieri n. sp. from the A. brevirostris (Olivier, 1811) group is described based on material dredged at depths of 198-408 m near the coasts of Papua New Guinea, Vanuatu and Madagascar. This species also occurs in the Philippines, based on morphological characters of a mutilated specimen from Masbate reported by Chace (1988). Alpheus alaincrosnieri n. sp. is unique within the A. brevirostris group, in having small orbital teeth. In most other features, A. alaincrosnieri n. sp. is morphologically closest to A. kagoshimanus Hayashi Nagata, 2000, A. longipalma Komai Ohtomi, 2018, A. macroskeles Alcock Anderson, 1894, A. nonalter Kensley, 1969 and A. acutocarinatus De Man, 1909. Alpheus vanuatu n. sp. is described based on several specimens dredged at depths of 231-331 m off Espirito Santo, Vanuatu. This species most likely represents a deep-water member of the newly defined A. paracrinitus species group, sharing most morphological characters with A. tenuipes De Man, 1910 and A. labis Banner Banner, 1982.