  We present work going on calculating the kaon B_K parameter in the 1/N_c
expansion. The goal of this work is to analyze analytically in the presence of
chiral corrections this phenomenologically very important parameter.
  We present the method used and preliminary results for the chiral limit value
for which we get the invariant \hat B_K^\chi=0.29 \pm 0.15. We also give some
analytical indications of why the large N_c prediction of \hat B_K= 3/4 may
have small 1/N_c corrections in the real case.
