This paper presents an analysis on the structural damping characteristics of polymeric composites containing dilute, randomly oriented nanoropes. The SWNT (single-wall nanotube) rope is modeled as a closed-packed lattice consisting of seven nanotubes in hexagonal array. The resin is described as a viscoelastic material using two models: Maxwell model and three-element standard solid model. The composite is modeled as a three-phase system consisting of a resin, a resin sheath acting as a shear transfer zone, and SWNT ropes. The "stick-slip" mechanism is proposed to describe the load transfer behavior between a nanorope and a sheath and between individual SWNTs. The analytical results indicate that the loss factor of the composite is sensitive to stress magnitude. It is illustrated that the "stick-slip" friction is the main contribution for the total loss factor of CNT-based composites even with a small amount of nanotubes/ropes.