A resistance training exercise device includes a stretchable cord having an internal cavity and a governor in the form of a limit band situated within that cavity and including first and second end segments. A retaining member attaches each of the end segments to the cord so as to impart stretching motion to the limit band when the cord is stretched during exercising. The retaining members provided at each end of the limit band each include a cup-shaped outer member and an inner, member having an outer peripheral surface. Each end segment of the limit band is positioned through an opening in the cup-shaped outer member and is secured to the inner member.