This paper firstly proves that if the sequence system has sensitive dependence on initial conditions and if sensitive constant of inferior limit is a positive number, then the limit system has sensitive dependence on initial conditions under strongly uniform convergence, gives an example to show that if the sequence system has sensitive dependence on initial conditions, then the sensitive dependence on initial conditions can not be kept by limit system under strongly uniform convergence, thus, derives that Auslander-Yorke chaos in sequence system does not have maintainability, secondly discusses that under strongly uniform convergence, sequence mapping of periodic point or almost periodic point of upper limit is contained in the limit mapping of periodic point or almost periodic point, and gives an example to show that sequence mapping of periodic point or almost periodic point of upper limit is not equal to the limit mapping of periodic point or almost periodic point.