  The application of the two-photon process pp -> pp + mu^+mu^- for the
luminosity measurements at LHC with the ATLAS detector is considered. The
expected accuracy of the absolute offline luminosity determination is 1 - 2 %
for the luminosity range of 10^{33} - 10^{34} cm^-2 s^-1. The preliminary cross
section estimates done for LHCb promise the same level of the luminosity
measurement accuracy at L = 2 x 10^{32} cm^-2 s^-1.
