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This work present a new class of Petri nets extended from systems of simple sequential processes with resources (S3PR)[J, Ezpeleta et al., 1995] for modeling manufacturing systems where only parts can interact with resources, and resources alone cannot interact with one another. The new class of net that is called ES3PR where deadlocks are related to unmarked siphons. ES3PR properly includes S3PR, augmented marked graphs and sub-classes of RCN merged nets where firing a transition may only generate parallel process for parts. As a result, ES3PR can model far more complex manufacturing process flows and resource sharing than these nets. We also present an algorithm of deadlock prevention for the class of Petri nets. The proposed method is an iterative approach by adding two kinds of control places called ordinary control place and weighted control place to the original model to prevent siphons from being unmarked. One is added a control place to an original net with its related arcs such that the controlled net is still an ordinary Petri net; the other is added a control place to the net with its related arcs such the controlled net become to a generalized Petri net. In addition, the weighted control place assures that there are no new unmarked siphons generated. We have obtained the relation of the proposed algorithm and the liveness and reversibility of the controlled net. Finally, a flexible manufacturing example is presented for illustrating the method.