This volume contains the proceedings of the 2nd International Conference on Discrete Mathematics and Theoretical Computer Science (DMTCS9) and the 5th Australasian Theory Symposium (CATS9). Both were held as part of the Australasian Computer Science Week (ACSW9) in Auckland, New Zealand, January 1999. The topics presented included those on: abstract data types and specifications; algorithms and data structures; automata and formal languages; computability and complexity; computational algebras, biology, geometry, logic, and number theory; concurrency, distributed systems, and parallel computing; constructive mathematics; discrete mathematics and combinatorial computing; formal semantics, specification, synthesis, and verification. These proceedings, comprised of 5 invited papers and 19 contributed refereed papers, thus provide the latest research in these fields.