CLIC is one of the current projects of high energy linear colliders. Vertical beam sizes of 1nm at the collision point and fast ground motion of a few nanometres impose an active stabilization of the final doublets at a tenth of a nanometre above 5Hz. The majority of our work concerned vibrations and active stabilization studies of cantilever and slim beams in order to be representative of the CLIC final doublets, which is one of the originality of the work. For that, we determined appropriate sensors and actuators, developed an active control algorithm, modelled the phenomenon, and finally constructed a prototype. In a first part, measured performances of different types of vibration sensors associated with an appropriate instrumentation showed that accurate measurements of ground motion are possible from 0.1Hz up to 2000Hz even if vibrations are low. Some non magnetic electrochemical sensors compatible with the specifications of CLIC can be incorporated in the active stabilization at a tenth of a nanometre. In a second part, a study of the impact of ground motion and of acoustic noise on beam vibrations showed that an active stabilization is necessary at least up to 1000Hz. In a last part, results on the active stabilization of our prototype at its two first resonances are shown down to amplitudes of a tenth of a nanometre above 5Hz by using in parallel a commercial system performing passive and active isolation from ground motion.