The connection between the Wigner distribution and the squared modulus of the fractional Fourier transform-which are both well-known time-frequency representations of a signal-is established. In particular the Radon-Wigner transform is used, which relates projections of the Wigner distribution to the squared modulus of the fractional Fourier transform. Moments of the Wigner distribution are then expressed in terms of moments of the fractional Fourier transform. Relations for the fractional Fourier transform moments are derived, and some new procedures are presented with the help of which Wigner distribution moments can be determined by using the fractional Fourier transform.