We have studied the spectra of several large earthquakes in the Chilean subduction zone using both accelerograms and CNSS instruments. For the two events studied here, the Iquique M_w 8.1 earthquake of 24 April 2014 and the M_w 6.9 Valparaiso earthquake of 24 April 2017 we observe similar features. For these earthquakes the velocity records at low frequencies obtained by integrating accelerograms agree quite well with the ground velocity derived from GNSS records at the same sites. These observations show that at low frequencies the ground spectra differ quite significantly from the usual Aki-Brune spectrum used in studies of the far-field spectral properties of earthquakes. The most important difference is that at short distances the near-field term of the source dominates the spectra at low frequencies. The near-field term in seismic radiation is proportional to the moment time function of the source which is very different from the moment rate function that controls farfield. The ground velocity spectrum is flat at low frequencies and proportional to the static displacement produced by the earthquke at the observation site. The displacement spectrum on the other hand has a low-frequency asympote proportional to omega – 1 instead of the usual flat spectrum predicted by the Aki-Brune model. More theoretical work is needed to identify the region where the near-field spectrum dominates.