In this paper, a network programming model with nonlinear cost functions is described along with computer-based algorithms for the solution of the network model. The network model described is general as it can be applied for the optimization of various physical, economic and social systems, e.g. water supply and wastewater system, traffice and transportation system, solid waste handling system, natural gas and petroleum pipelines, communication systems, etc. Realistic nonlinear cost functions reflecting economies-of-scale are use for flow through the area of the system network. The nonlinear cost functions are usually nonconvex in nature, and various complexities are encountered in minimization problems involving these functions, specifically the difficulty of obtaining globally optimum solutions. Two algorithms utilizing approximating iterative schemes developed during an ongoing research project are described in this paper. These algorithms have been applied with success in water supply planning and wastewater treatment and disposal system optimization.