1. A method for synchronizing transaction processing in a distributed database system with a plurality of sites, the system having at least one application site with a processor for executing an application program and an application requestor procedure, and a plurality of resource sites, each resource site including a server with a database and a data management processor, the method including the processor-executed steps of: operating at least one first resource site of the plurality of resource sites under control of a single-phase transaction synchronization procedure; operating at least one second resource site of the plurality of resource sites under control of a multi-phase transaction synchronization procedure; executing a transaction at the at least one application site, the transaction including at least one request for a database access operation at a resource site; issuing a transaction synchronization request from the application site and communicating the transaction synchronization request to the application requestor at the application site; determining at the application requestor whether any first resource sites performed database access operations during the transaction; and (a) if only one or more first resource sites performed database access operations during the transaction, communicating transaction commit requests from the application requestor to all such first resource sites, conducting single-phase transaction synchronization procedures at all such first resource sites in response to the transaction commit requests, and communicating results of such single-phase transaction synchronization procedures to the application site; otherwise, (b) if one or more first resource sites and one or more second resource sites performed database access operations during the transaction: first, communicating transaction commit requests to all such second resource sites and to the application requestor and commencing a multi-phase transaction synchronization procedure including all such second resource sites and the application requestor, communicating transaction synchronization requests from the application requestor to all such first resource sites, conducting single-phase transaction synchronization procedures at all such first resource sites in response to the transaction synchronization requests, and communicating results of such single-phase transaction synchronization procedures to the application site; followed by, completing the multi-phase transaction synchronization procedure and communicating results of the multi-phase transaction synchronization procedure to the application site; and either committing or backing out the transaction in response to results of transaction synchronization procedures communicated to the application site.