For a lumped parameter model of a flow network driven by a periodic generator. we apply averaging to find an approximate solution and analyze its stability. The approximate solution has three parts: mean flow due to the resistive effects of branches. a time-periodic part due to "inductive" effects, and a mean flow average correction due to the interaction of nonlinear and time varying effects. We present an example that may explain the scenario leading to venous diseases. It is shown that the widening of a branch in a venous network leads to an increase in the AC flow and a decrease in the DC flow through that branch, thus increasing the stress on venous valves. and consequently leading to a further increase in the effective width of the vein. (C) 2004 Elsevier Ltd. All rights reserved.