This paper deals with the influence of nanofiller on the behaviour of polymer dielectric in an electrical alternating field. As the basic polymer is selected a linear low-density polyethylene and as a nanofiller a perspective material based on aluminosilicates known as the Halloysite nanotubes is used. A broadband dielectric spectroscopy is applied as a diagnostic method. This method allows us to measure the real and imaginary part of the complex relative permittivity. The effect of different filling of polymer material with nanotubes to the ongoing polarization process is evaluated on the basis of the trend of the permittivity. Besides the influence of the simple presence of nanofiller, the effect of variable temperature is also taken into consideration. The measured data is evaluated as the frequency and temperature dependence with an emphasis on the interconnection of frequency and temperature effects. Subsequently, the data are processed as Cole-Cole diagrams (circular and linearized). These diagrams offer a slightly different view on the solved issue. The paper concludes with a calculation of the relaxation times of the polarization, which were registered in the selected frequency and temperature range. The relaxation times calculation is based on the theory of Cole-Cole diagrams. Linearized Cole-Cole diagram has been designed mainly for the calculation of relaxation times.