Polymer composites reinforced by carbon nanotubes have been extensively researched(1-4) for their strength and stiffness properties. Unless the interface is carefully engineered, poor load transfer between nanotubes (in bundles) and between nanotubes and surrounding polymer chains may result in interfacial slippage(1,2) and reduced performance. Interfacial shear, although detrimental to high stiffness and strength, could result in very high mechanical damping, which is an important attribute in many commercial applications. We previously reported(5) evidence of damping in nanocomposites by measuring the modal response (at resonance) of cantilevered beams with embedded nanocomposite films. Here we carry out direct shear testing of epoxy thin films containing dense packing of multiwalled carbon nanotube fillers and report strong viscoelastic behaviour with up to 1,400% increase in loss factor (damping ratio) of the baseline epoxy. The great improvement in damping was achieved without sacrificing the mechanical strength and stiffness of the polymer, and with minimal weight penalty. Based on the interfacial shear stress (similar to0.5 MPa) at which the loss modulus increases sharply for our system, we conclude that the damping is related to frictional energy dissipation during interfacial sliding at the large, spatially distributed, nanotube-nanotube interfaces.