The interactions between the main chain and lateral chains in grafted polymers play an important role on their dynamics. This is a complex issue, since several length scales are to be taken into account, from the local intramacromolecular interactions between linked moieties up to intermolecular interactions in phase separated systems. Such phenomena are investigated on the basis of new copolymers obtained by controlled radical polymerization. The effect of two parameters are studied separately, namely (i) the number of grafted chains on the main chain (cellulose acetate) and (ii) the length of grafted moieties (poly(methyl(diethylene glycol)methacrylate)). The dynamics of molecular motions was assessed by Low Frequency Mechanical Spectroscopy and Broad Band Dielectric Spectroscopy. The complex shear and dielectric moduli were measured on thin films (60m thickness) as a function of frequency and temperature. The sensitivity of these relaxation spectroscopy techniques, as compared to calorimetry measurements, allowed to study the effects of (i) the chemical structure of the copolymers and (ii) the microstructure at the nanoscale, as investigated by Small Angle X-ray Scattering. It is shownthat the main parameter is the soft grafted moities content: as expected the molecular mobility increases as the content of soft grafted chains increases. In addition, it is shown that this molecular mobility is drastically depressed by thermal treatment.