Résumé : When dealing with real systems, it is unrealistic to suppose that observations can be totally ordered according to their emission dates. The partially ordered observations and the system are thus both represented as finite-state machines (or automata) and the diagnosis formally defined as the synchronized composition of the model with the observations. The problem we deal with in this paper is that, taking into account partially ordered observations rather than sequential ones, it becomes difficult to consider the observations one after the other and to incrementally compute the global diagnosis. In this paper, we rely on a 'slicing' of the observation automaton and propose to compute diagnosis slices (for each observation slice) before combining them to get the global diagnosis. In order to reach this objective, we introduce the concept of 'automata chain' and define the computation of the diagnosis using this chain, first in a modular way and then, more efficiently, in an incremental way. These results are then extended to the case where observations are sliced according to temporal windows. This study is done in an off-line context. It is a first and necessary step before considering the on-line context which is discussed in the conclusion.