The first of the transfermium elements—those elements with an atomic number greater than 100—were discovered in the 1950s, largely by the Lawrence Berkeley Laboratory (LBL) in California and the Joint Institute for Nuclear Research (JINR) in Dubna, Russia. After each new element was claimed to have been discovered by one lab, the claim was contested by the other. The International Union of Pure and Applied Chemistry (IUPAC) and the International Union of Pure and Applied Physics (IUPAP) formed a joint working group to end the controversies, the Joint Neutral Group (JNG). When that group failed to resolve the discovery disputes, another was formed, the Transfermium Working Group (TWG). Neutrality was a value important to both groups, giving them the credibility necessary to act as mediators. For the JNG in the 1970s, and the TWG in the late 1980s, neutrality had different meanings and was attempted in different ways. The extensive use of archival collections in this paper provides a more complex and nuanced look at the geopolitical and disciplinary tensions surrounding these discovery disputes and the attempts at neutrality, in its different forms, to resolve them.