Techniques are described for managing access to computing-related resources that, for example, may enable multiple distinct parties to independently control access to the resources (e.g., such that a request to access a resource succeeds only if all of multiple associated parties approve that access). For example, an executing software application may, on behalf of an end user, make use of computing-related resources of one or more types that are provided by one or more remote third-party network services (e.g., data storage services provided by an online storage service)--in such a situation, both the developer user who created the software application and the end user may be allowed to independently specify access rights for one or more particular such computing-related resources (e.g., stored data files), such that neither the end user nor the software application developer user may later access those resources without the approval of the other party.