This volume contains the papers presented at the3rd International Wo- shoponRandomizationandApproximationTechniquesinComputer Science (RANDOM'99) and the 2nd International Workshop on - proximation Algorithms for Combinatorial Optimization Problems (APPROX'99), which took place concurrently at the University of California, Berkeley, from August 8-11, 1999. RANDOM'99 is concerned with appli- tions of randomness to computational and combinatorial problems, and is the third workshop in the series following Bologna (1997) and Barcelona (1998). APPROX'99 focuses on algorithmic and complexity issues surrounding the - velopment of e'cient approximate solutions to computationally hard problems, and is the second in the series after Aalborg (1998). The volume contains 24 contributed papers, selected by the two program committees from 44 submissions received in response to the call for papers, together with abstracts of invited lectures by Uri Feige (Weizmann Institute), Christos Papadimitriou (UC Berkeley), Madhu Sudan (MIT), and Avi Wigd- son (Hebrew University and IAS Princeton). We would like to thank all of the authors who submitted papers, our invited speakers, the external referees we consulted and the members of the program committees, who were: RANDOM'99 APPROX'99 Alistair Sinclair, UC Berkeley Dorit Hochbaum, UC Berkeley Noga Alon, Tel Aviv U. Sanjeev Arora, Princeton U. Jennifer Chayes, Microsoft Leslie Hall, Johns Hopkins U. Monika Henzinger, Compaq-SRC Samir Khuller, U. of Maryland Mark Jerrum, U. of Edinburgh Phil Klein, Brown U.