Fault diagnosis problem is discussed for discrete events systems described by partially observed Petri nets. Our goal is to detect and identify faults that may have occurred in both transitions and places assuming that we can measure some of them. The proposed approach is based on two mains steps (i) designing an algebraic observer for estimating the markings and the transitions of a partially observed Petri nets and (ii) presenting algorithms to detect and identify faults based on comparing the estimation of both the transitions and markings of the faulty system provided by an algebraic observer with those of the normal system. The effectiveness of the proposed approach is illustrated through a simple and a manufacturing example.