In the multi-core and multiprocessor domain, there has been considerable work done on scheduling techniques assuming that real-time tasks are independent. In practice a typical real-time system usually share logical resources among tasks. However, synchronization in the multiprocessor area has not received enough attention. In this paper we investigate the possibilities of extending multiprocessor hierarchical scheduling to support an existing synchronization protocol (FMLP) in multiprocessor systems. We discuss problems regarding implementation of the synchronization protocol under the multiprocessor hierarchical scheduling.