The report presents two mathematical models for use in water quality management and examines their application. A simulation model for predicting dissolved oxygen over a long reach of river based upon the Streeter-Phelps differential equations is described and examined as to its sensitivity to river depth and deoxygenation rate coefficient. Procedures for validating the simulation model are proposed. Additionally, a regression model for predicting water temperature as input to the simulation model is delineated. For given flow and temperature profiles on this long each of the Wisconsin River the simulation model calculates coefficients which attribute oxygen deficit to individual waste sources. A survey of stochastic programming techniques revealed that the problem of determining allowable waste discharges did not fit into existing techniques. A solution procedure for this semi-linear programming problem in which the objective function is a separable step function is presented. Use of these mathematical models in water quality management is discussed with special reference to their part in control systems and for calculating cost sharing plans. (Author)