TRAFFIC EQUILIBRIUM ANALYSIS HAS PROVIDED USEFUL VIEW IN TO THE TRANSPORTATION PLANNING PROCESS. EXISTING CONVEX PROGRAMMING APPROACHES, WHICH ARE EFFICIENT AND GUARANTEE CONVERGENCE, ARE RESTRICTED TO SINGLE COMMODITY FLOW problemS WITH INVERTIBLE DEMAND FUNCTIONS. IN THIS ARTICLE, WE FIRST SHOW THAT CONVEX PROGRAMMING APPROACHES CANNOT BE GENERALIZED TO BROADER, AND YET STILL REALISTIC, SETTINGS. SECONDLY, WE INTRODUCE A NEW APPROACH THAT CAN BE APPLIED TO MULTI-COMMODITY FLOW problemS WITH ARBITRARY DETERMINISTIC DEMAND FUNCTIONS. THE APPROACH CONSISTS IN FORMULATING THE TRAFFIC EQUILIBRIUM AS A NONLINEAR COMPLEMENTARILY problem. BASED UPON THIS FORMULATION, WE PROPOSE AND PROVE GENERAL EXISTENCE AND UNIQUENESS COMPUTATIONAL RESULTS ON A VARIETY OF TEST problemS TO ILLUSTRATE THE GENERALITY AND EFFICIENCY OF THE ALGORITHM.