Abstract: Strict stability and strict practical stability of nonlinear differential systems relative to initial time difference was analyzed by using differential inequalities technique. The concepts of stability of nonlinear differential equations with initial time difference was developed to strict stability of nonlinear differential equations with initial time difference. Several criteria of strict stability of nonlinear differential systems relative to initial time difference were given. A comparison principle with initial time unchanged was presented. By employing the presented comparison principle,  a new strict stability criteria of nonlinear differential equations with initial time difference was obtained