Abstract: In this paper a natural deduction system is suggested in which the hypotheses can beintroduced heuristicly.As a result,the system not only has the advantages that the ordinary naturaldeduction system has got,but also is easy to realize.In addition,it is possible to incorporate nonmonotonic reasoning into the system,as the system adopts the basic reasoning ways in which the hypotbeses can be introduced o(?) deleted.One goal of the paper is to try to give an idea of establishinga non-monotonic heuristic natural deduction system.