We provide a theorem for 1||Σ wjTj, which specifies necessary and sufficient conditions for adjacent job pairs in an optimum schedule. This 'adjacency theorem' is compactly stated and a straightforward proof is provided. The theorem unifies the related literature and generalises three disparate earlier research findings into a single simple result. Also provided is a brief description of how the theorem could be usefully applied in a search algorithm for 1||Σ wjTj.