Two new species of Taeniacanthus Sumpf, 1871 (Copepoda, Taeniacanthidae) are described from filefishes (Monacanthidae) caught in the Indo-West Pacific region: T. brayae n. sp. from Pervagor melanocephalus (Bleeker) collected from five localities within the Central Indo-Pacific realm and T. mcgroutheri n. sp. from Monacanthus chinensis (Osbeck) and Paramonacanthus choirocephalus (Bleeker) caught off the Australian coast. Taeniacanthus brayae n. sp. and T. mcgroutheri n. sp. are distinguished from their congeners by the presence of an elongate terminal endopodal segment of the antenna, a spinulated terminal process and one seta on the maxillary basis, six elements on the terminal exopodal segment of legs 2–4 and an armature of II, I, 2 and II, I, 1 on the terminal endopodal segments of legs 2 and 3, respectively. Taeniacanthus brayae n. sp. can be readily distinguished from T. mcgroutheri n. sp. by having one row (rather than multiple rows) of spinules on the large pectinate process of the antenna, four setae (rather than three) on the maxillule and a 3-segmented (rather than 2-segmented) endopod on legs 2–4. New host and/or locality records for the taeniacanthids Cirracanthus monacanthi (Yamaguti, 1939), C. spinosus Dojiri & Cressey, 1987, Nudisodalis acicula Dojiri & Cressey, 1987 and Taeniacanthus aluteri (Avdeev, 1977) parasitic on triggerfishes and filefishes, as well as supplementary morphological information for the females and the first descriptions of the males of C. monacanthi, C. spinosus and N. acicula, are also included.