  The exclusive production of one $\mu^+\mu^-$ pair in collisions of two
ultra-relativistic nuclei is considered. We present a simple method for the
calculation of the Born cross section for this process based on an improved
equivalent photon approximation. We find that the Coulomb corrections to this
cross section (corresponding to multi-photon exchange of the produced
$\mu^{\pm}$ with the nuclei) are small while the unitarity corrections
(corresponding to the exchange of light-by-light blocks between nuclei) 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 calculate 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 find that the inclusive
production of $\mu^+\mu^-$ pair coincides in this approximation with its Born
value.
