Hyperobjects are efficient mechanisms to coordinate accesses to shared variables and data-structures in task-parallel programming models, where each thread can operate on its own coordinated local view of the shared data. Synchronization between local views is restricted to occur at well-defined points in the execution, and can be left to the hyperobject implementation. This paper provides a general model for hyperobjects that does not require programming language or runtime support and may therefore be used with any task-parallel programming system. We show that hyperobjects can be efficiently implemented in a wait-free manner, meaning that all concurrent accesses to a hyperobject are guaranteed to complete in a bounded number of steps. The novel finisher hyperobject presented in this paper provides transitive termination detection for task-parallel programs. It can be used to efficiently implement task synchronization primitives like finish. However, finishers can also be used to manage reference-counted resources, e.g. shared pointers and copy-on-write pointers. Finally, we provide a wait-free variant of the associative reducer hyperobject known from the Cilk++ programming language.