In this paper, the vascular sounds of the arteriovenous fistula at the anastomosis and five centimeters downstream the anastomosis were analyzed. The analysis of the sounds was based on features extracted from the power spectral density (PSD) and wavelet decomposition. The database consists of 15 recordings at the anastomosis and 15 reference recordings obtained from 15 patients. The results showed that the vascular sounds at the anastomosis can be characterized as an extra energy in the higher frequencies (200-1000 Hz) i.e. higher mean frequency of the PSD than the reference recordings. Moreover, the wavelet decomposition of the anastomosis recordings showed a similar energy pattern, in the finer scales, to that found in studies of arterial and venous stenosis.