Some dynamical properties of the uniform limit dynamical system have been investigated. It has been found that for a sequences undefined of dynamical systems having same attractor undefined and converging uniformly to a dynamical system undefined the dynamical system undefined has the same attractor undefinedIt has been found that a sequence undefined of uniformly rigid dynamical systems converging uniformly to a dynamical system undefined the dynamical system undefined is also uniformly rigid. We have proved that the uniform limit undefined of a uniformly convergent sequence of dynamical systems having pseudo orbit tracing property has pseudo orbit tracing property. The expansiveness and the equicontinuous set ϵ: of the uniform limit dynamical system have been investigated.