In this report, we studied dielectric loss mechanisms in a 1-3 type of polymer nanocomposites, i.e., nanofibers or nanotubes in a polymer matrix. Sodium titanate nanotubes (TiNTs, 8-10 nm outer diameter and 300-500 nm long), which were synthesized by the hydrothermal method, were used as the fillers. The polymer matrix was a high permittivity relaxor ferroelectric polymer, poly(vinylidene fluoride-co-trifluoroethylene-co-chlorotrifluoroethylene). The nanocomposites were fabricated using solution-blending followed by hot-pressing above the melting temperature. Because of the high aspect ratio of TiNT fillers, the percolation threshold was found to be around 10-12.5 vol%. Below the percolation threshold, significant dielectric losses (both linear and nonlinear) were identified using bipolar and unipolar electric displacement - electric field (D-E) loop tests. For aggregated/percolated TiNTs, external electronic conduction was the major linear dielectric loss. For isolated TiNTs, internal electronic conduction contributed significantly to the nonlinear dielectric loss. From this study, we conclude that it is better to develop highly insulating nanofibers or nanotubes for the 1-3 type polymer nanodielectrics and the nanofillers content should be kept far below the percolation threshold in order to avoid significant dielectric losses. (C) 2016 Elsevier Ltd. All rights reserved.