||Analytical solutions are obtained for flows in downwardly inclined ducts, partly filled by a liquid and containing finite amplitude moving jumps. A unified theory for both roll waves and periodic slug flows in rounded ducts of arbitrary cross-section is worked out by means of some simplifications. The article is focused on slugs: a set of equations is obtained, which predicts the transition between roll waves and slug regimes and gives access to all flow characteristics without any need of closure laws concerning either the speed of propagation or the slug length. As a result, we gain a new insight on the physical structure of slug flow. The proposed model is valid for sufficient inclination, small pressure gradient along the duct and negligible superficial tension. Owing to assumptions, only main trends and orders of magnitude observed in experiments are to be checked. In this connection the model fits most of the previously published experimental results obtained in ducts of circular cross-section: the domain of occurrence of downwardly propagating slugs is satisfactorily predicted, the limitations in drift velocity and in liquid layer thickness are demonstrated and upwardly propagating slugs are possible.