Evolution of a.c. electrical properties under large strain of random nanocomposite materials made of a soft thermoplastic insulating matrix and hard conductive fillers is investigated. The transport properties are directly linked with the macroscopic mechanical strain on the composites during uniaxial tensile test or to the time under relaxation, meaning that the method is suitable for monitoring microstructural evolution of such composites. The real part of the conductivity indicated the breaking of the percolating network, while the imaginary part gave information on the possible `spatial correlation' of the damage events. Two different filler shapes were used, i.e. spherical and stick-like (aspect ratio about 15), leading to quantitatively different results. The microstructural evolution was simulated with the help of a resistance-capacitance (RC) model for the electrical properties and with finite element analysis for the mechanical properties.