We calculate the cross sections for the production of Higgs particles in association with a photon in $e^+ e^-$ collisions, $e^+ e^- to gamma+$Higgs, allowing for the longitudinal polarization of the initial electron and positron beams. We consider the associated production of both the Standard Model Higgs boson, and the neutral CP-even and CP-odd Higgs particles of its minimal supersymmetric extension. Complete and compact analytical expressions are given, and the size of the cross sections is illustrated for energies which will be reached at future $e^+ e^-$ colliders.
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