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XookSuut models circular and noncircular flows on resolved velocity maps. The code performs nonparametric fits to derive kinematic models without assuming analytical functions on the different velocity components of the models. It recovers the circular and radial motions in galaxies in dynamical equilibrium and can derive the noncircular motions induced by oval distortions, such as that produced by stellar bars. XookSuut explores the full space of parameters on a N-dimensional space to derive their mean values; this combined method efficiently recovers the constant parameters and the different kinematic components.