ABSTRACTA network design problem solves for link improvements or additions to an existing transportation network provided that a certain objective function such as social welfare is maximised. In addition, an equilibrium network design problem specifically requires each link to have user equilibrium flows.In this paper, two equilibrium transportation network design problems are formulated in a nonlinear bilevel programming framework; one with a budget constraint and one without. A bilevel programming formulation allows explicit consideration of the interaction between the public sector which supplies transportation facilities and the private sector which uses the given facilities. This paper presents a descent‐type algorithm to solve an equilibrium network design problem formulated in the nonlinear bilevel programming model for Korea. Numerical analysis using network data for a simplified Korean highway system is reporte