A heterogeneous distributed database system (HDDBS) is a system which integrates pre-existing databases to support global applications accessing more than one database. This paper outlines possible approaches to concurency control in 1LI)DBSs. The top-down approach emerges as a viable paradigm for ensuring the proper concurrent execution of global transactions ia an HDDBS. The primary contributions of this paper are the general schemes for local concurrency control wit11 pre-specified global serialization orders. Two approaches are outlined. The first is intended for performance enhancement but violates design autonomy, wbib the second does not violate local autonomy at the cost of generality ( it does not apply to all local concurrency control protocols). This study is intended as a guiding light through the maze of concurrency control in this new environment and enormous work remains to be doae.