  Mistake in FORTRAN program corrected. The numerical results and conclusions
are changed significantly: We present a calculation of the hadronic
light-by-light contributions to the muon $g-2$ in the $1/N_c$ expansion. We
have used an Extended NJL model and introduced an explicit cut-off for the high
energy region. We have then critically studied the relative size of the high
energy contributions. Although we find them large we can give a conservative
estimate of the light-by-light contribution to $a_\mu$ which is $-(11\pm5)
\cdot 10^{-10}$. This is between two and three sigmas the expected experimental
uncertainty at the forthcoming BNL experiment.
