  We study the simultaneous dissociation of heavy ultrarelativistic nuclei
followed by the forward-backward neutron emission in peripheral collisions at
colliders. The main contribution to this particular heavy-ion dissociation
process, which can be used as a beam luminosity monitor, is expected to be due
to the electromagnetic interaction. The Weizsacker-Williams method is extended
to the case of simultaneous excitation of collision partners which is simulated
by the RELDIS code. A contribution to the dissociation cross section due to
grazing nuclear interactions is estimated within the abrasion model and found
to be relatively small.
