They were part of Voorhoeve & McElhanon's original TNG proposal, but have been reduced in scope by half (nine families to four) in the classification of Malcolm Ross.
Voorhoeve argues independently for an Awyu–Ok relationship, and Foley echoes that Asmat may be closest to Awyu and Ok of the TNG languages.
Voorhoeve (1968) expanded on this and coined the name CSNG; his proposal added Trans-Fly and Marind to the mix.
Wurm's 1975 expansion of TNG also expanded CSNG, with the addition of Awin–Pa, Bosavi, Duna–Pogaya, East Strickland, Mombum, and Momuna.
Ross's recension in 2005 retained nothing from Voorhoeve and only Mombum from Wurm, though the Momuna languages were too sparsely attested for him to classify.