A new Boolean resubstitution technique with permissible functions and ordered binary decision diagrams (OBDDs) is presented. Boolean resubstitution is one technique for multilevel logic optimization. Permissible functions are special don't care sets. The data structure of permissible functions and logic functions at each node in Boolean networks is represented in terms of OBDD. Therefore, logic functions can be flexibly manipulated and rapidly executed. Boolean resubstitution was also applied to a multilevel logic synthesis. Results of experiments employing the improved OBDD operation and Boolean resubstitution techniques are presented.