Noncommutative planar particles: Higher order versus first order formalism and supersymmetrization

We describe the supersymmetrization of two formulations of free noncommutative planar particles - in coordinate space with higher order Lagrangian [1] and in the framework of Faddeev and Jackiw [2,3], with first order action. In nonsupersymmetric case the first formulation after imposing subsidiary condition eliminating internal degrees of freedom provides the second formulation. In supersymmetric case one can also introduce the split into "external" and "internal" degrees of freedom both describing supersymmetric models.