Ten species belonging to the genus Gonaxia Vervoort, 1993 occur in recent collections gathered by KANACONO (2016), KANADEEP (2017) and KANADEEP 2 (2019) expeditions of the French Tropical Deep-Sea Benthos Program in deep waters of the New Caledonian region. They were studied using the classical, morphological approach, supplemented by the first genetic characterization of the genus undertaken so far. Two species are previously undescribed, namely G. incisa Galea, sp. nov. and G. solenoscyphoides Galea, sp. nov. Additional notes on the remaining species are provided, notably the discovery of the female gonothecae of G. crassicaulis Vervoort, 1993 and G. perplexa Vervoort, 1993. Lofty colonies, with distinctive cladia-bearing branches spirally-arranged around the stem, assignable to the recently-described G. plumularioides Galea, 2016 actually represent fully-developed colonies of G. errans Vervoort, 1993, as demonstrated using molecular markers, the latter nominal species having priority. Its unusual, club-shaped, longitudinally-ridged gonothecae, fully free from the stem, are described for the first time. Supplementary notes on the hydrotheca of G. crassicaulis Vervoort, 1993 are provided, together with the description of a distinctive gutter of perisarc channeling the coenosarc of the colony along the lumen of both the stem and cladia. A multi-locus phylogenetic hypothesis of the Macrocolonia supports the establishment of the family Gonaxiidae Maggioni, fam. nov., to accommodate the species dealt with herein.