Abstract: Tethers of a tethered satellite system are divided into manytether segments,say M-1 segments altogether,so that the tension oneach segment can be considered as a constant By using the characteristicsof the intermediate junction points,the M-point boundary value problemcan be reduced to a two-point problem,and frequencies of coupled in-plane vibrations of the system can be determined by evaluating 4thdeterminants.By the concept of the centre of motion,an accurate expres-sion for tether tension is derived and used in determining frequencies.The method can be applied to all N-body(N≥2)tethered satellite systems.