The synonym fish names, which have not checked in when using scientific names and referring at several publications, is negatively impacted on name definition and classification of fishes. Therefore, the paper aims to provide scientific names of the eels and morays in the Vietnamese marine waters completely and exactly. Many of fish species belonging to Anguilla of family Anguillidae (order Anguilliformes) are rearing objects, beside they also are exported objects and have high economic value. However, they are being overexploited that makes the resource decreasing sharply. Some fish speices of genus Anguilla were listed in Vietnam Red Book. Forty eight documents published during 1974-2012 listed 169 species names belonging to 37 genera and 12 families of the order Anguilliformes in different ecological marine waters in Vietnam. This study corrected, updated and confirmed the species composition of the eels and morays in the Vietnamese marine waters with 96 species belonging to 34 genera and 9 families. The results play important roles of biodiversity assessment and marine fish protection.