Strong and sustained winds on Mars have been considered rare, on the basis of surface meteorology measurements and global circulation models, raising the question of whether the abundant dunes and evidence for wind erosion seen on the planet are a current process. Recent studies showed sand activity, but could not determine whether entire dunes were moving--implying large sand fluxes--or whether more localized and surficial changes had occurred. Here we present measurements of the migration rate of sand ripples and dune lee fronts at the Nili Patera dune field. We show that the dunes are near steady state, with their entire volumes composed of mobile sand. The dunes have unexpectedly high sand fluxes, similar, for example, to those in Victoria Valley, Antarctica, implying that rates of landscape modification on Mars and Earth are similar.