Three volcanic rock associations — identified by the geographic acronyms TLTF, MRB, and SBS — can be recognized in seven late Cenozoic provinces at convergent plate boundaries in Papua New Guinea. These associations are distinguished on a variation diagram showing the Differentiation Index relative to normative nepheline or to normative quartz plus the silica of normative hypersthene; this diagram serves as the basis for a preferred scheme of volcanic rock nomenclature for arc-trench systems. Rocks of the TLTF group constitute a dominantly alkalic (nepheline-normative) association. In contrast, the MRB and SBS groups do not correspond to any of the associations widely postulated for other circumoceanic regions. Calc-alkalic–type rocks, for example, are found in both associations: in the MRB group they form compositional continua with shoshonitic rocks, and in the SBS group they form continua with tholeiitic ones. We suggest that circumoceanic rocks should not be classified into these artificial, world-wide, “standard” associations; a more meaningful method is to identify associations on a regional basis. However, the most useful procedure would be to correlate the same ranges of rock compositions and relative abundances of rock types in individual tectonic provinces with specific geodynamic features or source-region compositions. These correlations may lead to the recognition of natural rock associations on a world-wide basis.