In High-Level Architecture, federates are integrated into a federation in single Run-Time Infrastructure middleware, which handles High-Level Architecture services for interoperation. The interoperation of federations is required in order to combine systems simulated in existing federations. Unlike a single federation, the interoperation of federations provides the data security and makes it possible to interoperate federates developed in different Run-Time Infrastructures. Previous research has used a proxy method to interoperate federations without modifying the Run-Time Infrastructure. Based on the proxy method, this paper proposes a form of High-Level Architecture service management for the interoperation of federations. Federations construct a twotwo-level hierarchical federation that uses proxies to interoperate different levels and that defines the data structure for interoperation and data security. For each High-Level Architecture service protocol, we propose the algorithms of the proxy and show how the service protocol works in the two-level hierarchical federations. In addition, the proxy handles the race condition, which may occur in interoperation of federations, and describes how to solve it. The algorithms are verified theoretically, and a case study shows the practical application for the interoperation of federations.