  A twistor model is proposed for the free relativistic anyon.
  The Hamiltonian reduction of this model by the action of the spin generator
leads to the minimal covariant model; whereas that by the action of spin and
mass generators, to the anyon model with free phase space that is a cotangent
bundle of the Lobachevsky plane with twisted symplectic structure. Quantum
mechanics of that model is described by irreducible representations of the
(2+1)-dimensional Poincare' group.
