We present the first-order coherent exclusive exponentiation (CEEX) scheme,
with the full control over spin polarization for all fermions, In particul
ar it is applicable to difficult case of narrow resonances. The resulting s
pin amplitudes and the differential distributions are given in a form ready
for their implementation in the Monte Carlo event generator. The initial-f
inal state interferences are under control. The way is open to the use of t
he exact amplitudes for two and more hard photons, using Weyl-spinor techni
ques, without giving up the advantages of the exclusive exponentiation, of
the Yennie-Frautschi-Suura type. (C) 1999 Elsevier Science B.V. All rights
reserved.