In order to improve the global saf sty and reliability level of multi-phase production systems and to guarantee their economical efficiency, we need a better understanding and control of hydraulic instabilities observed at the outlet of multi-phase sea-lines. This may be obtained through the development of slug flow stochastic models, which must be able to explain: (a) The generation of the various types of slug length distributions which are observed on experimental data sets. (b) The evolution of these distributions along the sea-lines up to their outlets, where large hydraulic fluctuations may be dangerous for the treatment installations. Based on experimental as well as theoretical arguments, we present such a model with emphasis on slug generation. We give a detailed theoretical analysis, together with a discussion of the underlying assumptions which justify the introduction of this model.