Thirty-four new species of Rhagovelia are described from the East Papua Composite Terrane of far eastern New Guinea. The new taxa described from this area are as follows: R. yela, R. woa, and R. mbo from Rossel Island; R. tagula, R. kolukolu, and R. riu from Tagula Island; R. bwagabwaga from Misima Island; R. suloga from Woodlark Island; R. torrenticola and R. elongata from Goodenough Island; R. awaetowa from Fergusson Island; R. dibuwa from Normanby Island; R. basima from Fergusson and Normanby islands; R. kalawai from Sideia and Basilaki islands; R. guiagoila from Basilaki, Sideia and Sariba islands; R. tufi, R. bowutu, R. obscura, R. upalai, R. antap, R. goilala, R. udabe, R. watuti, R. peninsularis, R. auga, R. aviavi, R. tekadu, R. sapoi, R. mimani, R. dinga, R. ivimkana, R. loriae, R. grisea, and R. cheesmanae from the Owen Stanley Range of eastern New Guinea. Redescriptions are also provided for five previously described species occurring in this portion of New Guinea: R. peggiae Kirkaldy, R. hirsuta Lansbury, R. priori Lansbury, R. caesius Lansbury and R. aureospicata Lansbury. A regional key is provided for these 39 species of Rhagovelia occurring in the Papuan Peninsula and adjacent island groups, accompanied by figures of the male parameres and other diagnostic morphological structures, and distribution maps for all species.