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A space tether is a long cable used to couple satellites, probes or spacecrafts to each other or to other masses, such as a spent booster rocket, space station, or an asteroid. The motorised momentum exchange tether (MMET) was first proposed by Cartmell in 1996 and published in 1998. The system comprises a specially designed tether connecting two payload modules, with a central launcher motor. The models in this book have shown that including axial, torsional and pendular elasticity, the MMET systems have a significant bearing on overall performance and that this effect should not be ignored in future, particularly for control studies. This book provides the following points: introduction to space tethers and space tethers control, the motorised momentum exchange tether(MMET), hybrid fuzzy sliding mode control for spin-up of the MMET. The studies should help shed some light on the tether systems and hybrid control for the tether spin-up, and should be especially useful to professionals in reospace/mechanical/control engineering, or anyone else who may be of interest in utilising intelligent control for dynamical behaviors of the space tethers.