Due to changes in physical characteristics, the valley side of a drainage basin may be represented by a series of overland planes. In such a situation, the downstream outflow from one plane becomes the upstream inflow for the subsequent plane. Based on the kinematic wave equations, two time of concentration (time to equilibrium) formulae are derived for planes subject to uniform rainfall excess and with a constant upstream inflow. For practical applications, the formulae are further developed in terms of the Manning resistance coefficient. The derived formulae are all consistent with those published for the case of zero upstream inflow.