Composite materials are broadly recognized and accepted in a variety of engineering applications due to their inherent properties such as higher stiffhess, good corrosion resistance and more importantly assisting weight reduction. Shafts made of composite materials are widely the subject of study as it incurs the advantage of the above said properties. The composite drive shafts which can give an increased natural frequency for the same length as that of the steel shaft is a potential candidate in eliminating two piece steel drive shaft. It is used as transmission shaft in marine pro-pulsion and many other applications where weight reduction is very much appreciable. The vital rotor dynamic characteristics require for any shaft system are the natural frequencies in essentially in bending and torsion modes, the response studies and the torque transmission characteristics. In this work, glass/epoxy and carbon/epoxy shafts are studied for their response behaviour using harmonic analysis. Unbalance response studies is carried out in composite shafts by developing an un-balance in the disc mass which is equal to the eccentric mass times the radius. The shafts are modeled using glass and carbon fibers with epoxy resin as the matrix material. The modeled shafts are studied with discs mounted on them. Glass, carbon and steel discs are used for the response study. The shaft and disc combinations are varied and the results are compared. The work is carried out using ANSYS. Apart from glass and carbon shafts, hybrid shafts which include both the glass and carbon fibers in a single shaft model are also used for the study. As the hybrid shafts include the advantage of both fiber materials, it is a more viable model in order to achieve characteristics to suit respective applications. The response behavior of hybrid shafts with different discs is analyzed and compared with the glass/epoxy and carbon/epoxy shafts.