Because water pollution is a stochastic process, water quality standards must incorporate variability. After reviewing previous deterministic models, the document generalized and extended earlier stochastic models. In particular, the project expanded and verified the Custer and Krutchkoff model. The specific objectives were to: Adapt the model to accept variable or random input loadings; Adapt the estuary model to treat segmented estuaries; Verify the adapted models with data supplied by WQO; Find a method for using data to estimate and predict the stochastic parameter delta. The objectives were successfully achieved and verification accomplished with data from the Ohio River and the Potomac Estuary. The report concluded that the extended Stochastic Model can handle load inputs, rate constants, velocity, temperature, benthal demands, land runoff, hydraulic parameters, geometry, and random pollution inputs. It can accurately predict the time-dependent mean concentration in a transient state condition or pseudo-steady state condition at any point in a stream or estuary. Further, the proportion of time that the BOD, DO and nitrogen concentrations will be above or below any given level can also be predicted accurately. Recommendations were made for further use and expansion of the model. (Author)