The U.S. Army Engineer Division, Ohio River, is responsible for maintaining a navigable channel on the Ohio River during low-flow periods through the manipulation of the navigation dams on the river. In addition, during periods of flooding on the lower Ohio and lower Mississippi Rivers, the Ohio River Division directs the operation of Barkley and Kentucky Reservoirs on the Cumberland and Tennessee Rivers, respectively. Flood control regulations by these reservoirs are met by controlling, to some degree, the Ohio River stage at Cairo, Illinois. A mathematical model, SOCHMJ, for unsteady-flow solutions in multi-junction systems has been modified to include the effect of five navigation dams on the Ohio River in addition to the effect of operations at Barkley and Kentucky Reservoirs. For economical applications of the model to the system extending from Louisville, Kentucky, on the Ohio River, Livermore, Kentucky, on the Green River, Mt. Carmel, Indiana, on the Wabash River, Barkley Dam on the Cumberland River, Kentucky Dam on the Tennessee River, and Cape Girardeau on the upper Mississippi River to Caruthersville on the lower Mississippi River, the model has been modified to accept two time steps. A large time step applies to large branches, whereas a smaller time step is used to step computations forward on small branches within the large time step. An initial calibration of the model to 1975 data has been completed with encouraging results. Similar results from an application using 1976 data with no additional calibration of the model are also presented. (Author).