The current document is directed to methods for aggregating host computers into distributed computing systems and to distributed computing systems created by the methods. In a described implementation, host computers are aggregated into two or more clusters, at a first distributed-computing-system level, each managed by a second-level management server. The two or more clusters are then, in turn, aggregated into a hierarchical distributed computing system managed by a top-level management server. The top-level management server is interconnected to, and accesses, the second-level management servers through a host-gateway appliance that includes host-gateway control logic implemented within a server computer. In order to achieve scalability and efficiency, the top-level management server provides a subset of the native management commands to system administrators and other users who access a management interface provided by the top-level management server.