This paper provides a regularity theorem for some 4n￣(th)-order linear nonsymmetric or nonlinear differential operator that arises in considering certain types of moving behaviors of some objects, which includes two homeomorphism and extended homeomorphism classes in real (nolinear) case or contains three linear homeomorphism and extended linear homeomorphism classes in complex (linear) case. It is useful to illustrate some stabilities in both directions of certain objects(such as some flying apparatus)in their moving processes.