  The exclusive production of one $\mu^+\mu^-$ pair in collisions of two
ultra-relativistic nuclei is considered. We present the simple method for
calculation of the Born cross section for this process. Then we found that the
Coulomb corrections to this cross section (which correspond to multi-photon
exchange of the produced $\mu^{\pm}$ with nuclei) are small while the unitarity
corrections are large. This is in sharp contrast to the exclusive $e^+e^-$ pair
production where the Coulomb corrections to the Born cross section are large
while the unitarity corrections are small. We calculated also the cross section
for the production of one $\mu^+\mu^-$ pair and several $e^+e^-$ pairs in the
leading logarithmic approximation. Using this cross section we found that the
inclusive production of $\mu^+\mu^-$ pair coincides in this approximation with
its Born value.
