The concept of flight-path stability, which is today in use, is based on the characteristics of steady unaccelerated flight conditions, and so can be called “static flight-path stability.” After the description about the “static flight-path stability, ” this paper introduces the “dynamic flight-path stability” concept for accelerated/decelerated flight conditions, and discusses the necessary elevator-compensation to provide an airplane with the designated dynamic flight-path stability. Furthermore, it is demonstrated that the airplane with the compensation can stably control the flight-path by the elevator in the backside flight region, through the study on the airplane's response and phugoidmode characteristics.