Abstract. Monitoring large distributed concurrent systems is a challenging task. In this paper we formulate (model-based) diagnosis by means of hidden state history reconstruction, from event (e.g. alarm) observations. We follow a so-called true concurrency approach: the model defines explicitly the causal and concurrency relations between the observable events, produced by the system under supervision on different points of observation. The problem is to compute on-the-fly the different partial order histories, which are the possible explanations of the observable events. In this paper we extend our first method based on Petri nets unfolding to high-level parameterized Petri nets. This allows the designer to model data aspects (even on infinite domains) and non deterministic actions. The observation of such an action gives only partial information and the supervisor has to introduce parameters to represent the hidden aspects of the reached state. This supposes that the possible values...