Coherent exclusive exponentiation CEEX: the case of the resonant $e^+ e^-$ collision

We present the first-order coherent exclusive exponentiation (CEEX) scheme, with the full control over spin polarization for all fermions. In particular it is applicable to difficult case of narrow resonances. The resulting spin amplitudes and the differential distributions are given in a form ready for their implementation in the Monte Carlo event generator. The initial-final state interferences are under control. The way is open to the use of the exact amplitudes for two and more hard photons, using Weyl-spinor techniques, without giving up the advantages of the exclusive exponentiation, of the Yennie-Frautschi-Suura type.