The homogeneous composites of single-wall carbon nanotube (SWNT) and Stycast 1266 epoxy were made with the nanotube concentrations of 0.01–0.21 wt % by using a high frequency sonication method. Direct current conductivities of various mass fractions show typical percolation behavior and the percolation threshold pc is found to be 0.074 wt % and the conductivity exponent t is estimated as 1.3±0.2. The anomalously small pc is attributed to the large aspect ratio of the nanotubes. Dielectric measurement was performed at temperatures 220–300 K with the frequency range of 20 Hz–1 MHz. There appeared different dielectric aspects according to the mass fractions p≪pc, p∼pc, or p≫pc. The dielectric relaxation of epoxy dominates at low concentrations (p≪pc), while at high concentrations (p≫pc) we found a scaling property in the frequency dependence of loss tangent. The scaled loss tangent spectra show a Debye type relaxation. Near the percolation threshold (p∼pc), the composites show peaks in the frequency dependence of the imaginary part of their electric moduli. Log–log plots of ac conductivity versus frequency for the midrange (p∼pc) composites exhibit the scaling and universal behavior regardless of temperature and mass fraction of SWNT. © 2003 American Institute of Physics.