Carbon nanotubes (CNTs) and graphene nanosheets (GNSs) were used as fillers in epoxy composites with the aim of increasing the electrical and thermal conductivities of the composites. The filling of pristine CNTs produced the highest electrical conductivity (sigma), whereas a high CNT functionalization and the two-dimensional planar structure of GNSs were promising for improving the thermal conductivity. A combination of CNTs and GNSs exploited the advantages of both. When the CNT fraction was larger than 50 wt %, a higher sigma was obtained. When a small amount of functionalized CNTs was added to the GNSs, the thermal conductivity was also increased. The rheological measurements revealed the lowest complex viscosity for the GNS filling and showed the exciting advantages of an easy processing. As a result, the mixed filling also exhibited a much lower viscosity than the pure CNT fillings. (c) 2013 Wiley Periodicals, Inc. J. Appl. Polym. Sci., 2013