In modeling a discrete event system, the map from physical system to logic system may be not complete due to the complex behaviors of the system. In this paper, the concept of incomplete model is introduced. Next, a method for judging diagnosability in incomplete model is proposed, and the corresponding on-line version of the method is also presented. Incomplete behaviors can be added to the model, and makes the model complete. Offline diagnosability is judged by classical twin-plant method. According to the ordered observations and prefix of language, the incomplete behaviors are judged and disposed. With an additional method that judge incomplete behaviors, the incomplete behaviors are added into model, and the online diagnosability is judged incrementally in twin-plant by incomplete behaviors. By judging diagnosability online, whether a fault can be found exclusively by limit observations is decided. The proposed methods suit for the systems which is discrete.