The equilibria based on a situation in which two or more profit-maximizing private firms operate multiple toll roads in a road network are examined. The profits are interrelated because of demand interdependence in the network. A competitive game model is developed to analyze the strategic interactions between the private toll road operators in determining their supply (road capacity) and price (toll level) over the network. A simple but representative case of two competitive firms, each providing a single toll road (corresponding to a single link) on the network, is considered in which the two toll roads are either substitutable or complementary in terms of their demand interdependence. A quasi-Newton method in conjunction with a sensitivity analysis method of equilibrium network flow is used to determine the competitive game solutions subject to network equilibrium constraints.