This paper deals with the incremental off-line computation of diagnosis of discrete-event systems. Traditionally, the diagnosis is computed from the global automaton describing the observations emitted by the system on a whole time period. The idea of this paper is to slice this global automaton according to temporal windows and to compute local diagnoses for each of these windows. It is shown that, under some conditions, the global diagnosis can be computed from the local diagnosis. This paper presents the formalization used to compute an incremental diagnosis, relying on the new concept of automata chain. It is then shown that it is possible to take into account the diagnosis obtained for the previous temporal windows to incrementally compute the current diagnosis more efficiently. This work is a first and necessary step before considering the on-line diagnosis computation. The main difficulty is then to ensure the correct slicing of the observation automaton and to determine the a...