This study exposed results of investigations on the two-fluid laminar-laminar stratified flow in an inclined channel. Multi-holdup regions have been mapped and visualized in a new way by plotting solution surface of the holdup equation. This representation clearly exhibits the link between backflow situation and multiple holdup solution occurence. The multiple solution problem can be addressed following different approaches. First, the solutions of the two-fluid system are interpreted in term of the minimization of a potential function. Secondly, the minimization of the dissipation rate at the feasible holdup is investigated and thirdly, a long-wave stability analysis is considered. (C) 2015 Elsevier Ltd. All rights reserved.