1. A method, in a data processing system having a plurality of processors and a memory, for handling conflicts in a transactional memory system, comprising: executing, by the plurality of processors, threads in the data processing system in a first conflict resolution mode of operation in which threads execute conflicting transactional blocks speculatively; determining, by a processor of the plurality of processors, for a transactional block, if the first conflict resolution mode of operation is to be transitioned to a second conflict resolution mode of operation in which threads accessing conflicting transactional blocks are executed serially and non-speculatively; and executing, by the processor, a thread that accesses the transactional block using the second conflict resolution mode of operation in response to the determination indicating that the first conflict resolution mode of operation is to be transitioned to the second conflict resolution mode of operation.