A method and apparatus for estimating a flow rate of a phase of a multiphase fluid is disclosed. A first velocity distribution is obtained for a first set of nuclei in the fluid from a Nuclear Magnetic Resonance (NMR) signal received for the fluid in response to a first NMR excitation signal. A second velocity distribution is obtained for a second set of nuclei in the fluid from an NMR signal received for the fluid in response to a second NMR excitation signal. A velocity of the phase is estimated from the first velocity distribution and the second velocity distribution. The flow rate of the phase is estimated using the estimated velocity of the phase and an estimated volume fraction of the phase.