  We calculate the hadronic light-by-light contributions to the muon $g-2$. We
use both $1/N_c$ and chiral counting to organize the calculation. Then we
calculate the leading and next-to-leading order in the $1/N_c$ expansion low
energy contributions using the Extended Nambu--Jona-Lasinio model as hadronic
model. We do that to all orders in the external momenta and quark masses
expansion. Although the hadronic light-by-light contributions to muon $g-2$ are
not saturated by these low energy contributions we estimate them
conservatively. A detailed analysis of the different hadronic light-by-light
contributions to muon $g-2$ is done. The dominant contribution is the twice
anomalous pseudoscalar exchange diagram. The final result we get is $a_\mu^{\rm
light-by-light}= (-9.2\pm3.2 ) \cdot 10^{-10}$. This is between two and three
times the expected experimental uncertainty at the forthcoming BNL muon $g-2$
experiment.
