Until now, almost all investigations of asynchronous iterations within domain decomposition frameworks targeted methods of the parallel Schwarz type. A first, and sole, attempt to deal with a primal substructuring framework resulted in an asynchronous substructuring method where relaxation occurs simultaneously on the subdomains and on the interface between them, which therefore corresponds to a substructured relaxation scheme defined on the whole global domain. In this paper, we propose a Gauss–Seidel kind of improvement consisting of alternating between relaxation on the interface and relaxation on the subdomains, hence, always using the latest solutions in the subdomains when updating the solution on the interface, which is feasible at no additional cost. It turns out that one particular case of our general alternating relaxation scheme corresponds to an asynchronous substructuring method with iterations fully defined on the subdomains’ interface, and where only local Schur complements are involved. Practical performance evaluation on both standard Poisson’s and linear elasticity problems has been conducted using a multi-node parallel computational platform with up to 720 CPU cores.