  We estimate the velocity field in a large set of $N$-body simulations
including massive neutrino particles, and measure the auto-power spectrum of
the velocity divergence field as well as the cross-power spectrum between the
cold dark matter density and the velocity divergence. We perform these
measurements at four different redshifts and within four different cosmological
scenarios, covering a wide range in neutrino masses. We find that the nonlinear
correction to the velocity power spectra largely depend on the degree of
nonlinear evolution with no specific dependence on the value of neutrino mass.
We provide a fitting formula, based on the value of the r.m.s. of the matter
fluctuations in spheres of $8h^{-1}$Mpc, describing the nonlinear corrections
with 3\% accuracy on scales below $k=0.7\; h$ Mpc$^{-1}$.
