Abstract: In Petri net,the introduction of the concept fairness is to discuss the relationship of two transitions happened in net system．This relationship can well reflect whether each part of the concurrent system in the competition for resource has starvation-free problem．According to the definition and the relation of the weak fairness and fairness,it was proved that fairness can be deduced by weak fairness for a bounded Petri net and for two classes unbounded Petri net．Fairness cannot be deduced by weak fairness for other unbounded Petri net．

Key words: Petri net,Weak fairness,Fairness,Boundedness