The increasing number of power electronic devices in electrical grids may lead to harmonic distorted voltages, which are considered to be possible causes of component failures. In this study, the dielectric losses of epoxy polymer and functionally filled silicone rubber (f-SiR) samples are investigated under harmonic distorted voltages in terms of their dielectric losses and the consequent heat source density within the material. The results suggest that the epoxy polymer samples behave linearly to the electric field strength and therefore allow good predictability of the dielectric losses. The investigated f-SiR samples exhibit a nonlinear behaviour when an electric field threshold is exceeded. The subsequent direct loss measurements under harmonic distorted voltage reveal a sharp rise of the dielectric loss with increasing electrical field strength. This leads to a higher risk of excessive heat in the material when harmonics are present. In conclusion, the investigation highlights the difficulties of estimating dielectric losses in nonlinear dielectric materials when distorted voltages are present.