The goal of the work is to investigate the mutual influence of the tether vibrations and the vibrations of flexible appendages during thrusting phase. A mathematical model of the space tug and the towed space debris with flexible appendages is developed. Parameters of the system are determined with assumptions that the system is moving in straight line, avoiding high amplitude vibrations of flexible appendages. The expression of the discriminant indicates that the vibrations of the tether and flexible appendages influence each other. A critical tether stiffness exists for the given space tug mass that should be avoided.