Nanocomposite polymer electrolytes based on a fully amorphous polymer electrolyte (trihydroxypoly(ethylene oxide-co-propylene oxide), known as 3PEG, with LiClO4 salt) were studied by means of small-angle neutron scattering with the aim to clarify how the filler particles (nanosized TiO2 or Al2O3) are distributed in the polymer. The scattering data show that the particles are not well dispersed but aggregate in fractal, polymer-like structures. The structures, with a fractal dimension of similar to 2 on length scales from 100 nm up to at least 400 nm, consist of branched chains which are about 1-2 primary particles wide (similar to 40 nm for TiO2 and similar to 30 nm for Al2O3). The obtained results provide structural support for the hypothesis of earlier works that the ionic conductivity increase observed in nanocomposite polymer electrolytes is due to the formation of a percolating layer close to the filler particles with higher conductivity.