This volume contains a selection of papers presented at the Fifth Franco-Belgian Meeting of Statisticians, held in Luminy-Marseille (France) on November 23-24, 1984. The diversity of these papers reflects the broadness of the topic of the meeting : the asymptotic theory for non i.i.d. processes. First of all, asymptotic theory is focused on various types of convergence : almost sure convergence, convergence in distribution and convergence in variation. In an other direction, relaxing the hypothesis of i.i.d. processes leads to consider a large variety of situations, characterized either by hypotheses on the marginal model (i.e. after integration with respect to parameters or exogenous variables) such as stationarity, exchangeability of Markovian property or by assumptions on the model conditionally on exogenoous variables. The main tools used in such situations are martingale theory and the ergodic theorem. They may be applied in various situations such as posterior expectations in Bayesian analysis, rational expectations, generalized residuals and mixing conditions in conditional models or predictions in nonstationary q-dependent processes. All the above concepts are met both theoretically and through applications in the present volume.