Thirty-nine species are recognized of which twenty-four are described as new ( K. bullata, K. carrii, K. chimbuensis, K. ferox, K. flagelliformis, K. fragrans, K. fugax, K. hartleyi, K. karengana, K. katikii, K. kostermansii, K. latifolia, K. leachii, K. macrantha, K. nitens, K. novobritanica, K. oblongata, K. rosselensis, K. royenii, K. shungolensis, K. sleumeri, K. streimannii, K. sudestensis, and K. versteeghii) ). One new combination is made: K. oligocarpella (Kaneh. & Hatus.) Philipson, and several species are reduced to synonymy. Thirty-six species occur in New Guinea, all but three of these being endemic to that island group. A key to the species is provided and their geographical ranges are given.