In this paper, we examine the monitoring of a moving interface problem in immiscible floods in 1-D heterogeneous systems. The solution is presented for monitoring saturation fronts in an extended case of a classical 1-D Buckley Leverette with various lateral permeability profiles. Flood is assumed to be at a constant injection rate but with the opportunity to continuously monitor injection pressure, fractional composition of produced fluid and production pressures. Lateral changes in effective transmissibilities between the injector and the producers caused by movement of immiscible fluid-fluid interface and detected from the solution of interference pressure equation provide an added dimension for tracking the saturation fronts. The effect of the rock heterogeneities is filtered out by analysis of the incremental changes observed with respect to the base measurements at the early stages of the flood.