  We discuss production of two $\mu^+\mu^-$ pairs in ultraperipheral
ultrarelativistic heavy ion collisions at the LHC. We take into account
electromagnetic (two-photon) double-scattering production and for a first time
direct $\gamma\gamma$ production of four muons in one scattering. We study the
unexplored process $\gamma \gamma \to \mu^+\mu^-\mu^+\mu^-$. We present
predictions for total and differential cross sections. Measurable nuclear cross
sections are obtained and corresponding differential distributions and counting
rates are presented.
