Progress on the development of a mathematical model and associated computer programs for use by the Illinois State Library in evaluation and planning of the interlibrary loan (ILL) network is summarized. Pertinent published literature on ILL networks is reviewed in terms of network structure, operations, satisfaction of requests, and costs. A flow chart model of the Illinois ILL network is outlined, and then alternate approaches are considered for the mathematical modeling of an ILL network. Network flow theory and simulation are discarded in favor of a hierarchical queueing network which will be analyzed using approximations that will be validated with simulation. An initial version of this model, named ILLINET, has been programed into an on-line interactive package where the user can input alternative network operating policies and test the effect on average delay in satisfying a request, probability of satisfying a request, total network operating costs, and unit costs. Six possible hardware applications of computer and communications technology are discussed, ranging from simple telephone and WATS line to the possible use of a computer to control the whole network. (Author/SL)