The objective of this study was to use generalized initial conditions to find the downstream proablity distributions of pollution defined as biochemical oxygen demand (BOC) and dissolved oxygen (DO) for particular times of travel, The results were based upon assumptions of previous workers and, in addition, an assumption of independence of BOD and DO. This was necessary in order to obtain the DO marginal probability distribution from the appropriate joint distribution. A study of independence indicated that this assumption did not invalidate the results. The resulting program is more versatile than previous programs in that, by use of generalized initial conditions, the stream analysis has the capability of handling changes in stream parameters and the introduction of major pollution sources at several points downstream. The final result is a computer program designed to compute the BOD and DO probability0 distributions.