  Construction of future Muon Collider tangential to the Large Hadron Collider
will give opportunity to realize mu-p collisions at multi-TeV center of mass
energies. Using nominal parameters of high luminosity and high energy upgrades
of the LHC, as well as design parameters of muon colliders, it is shown that
L_mu-p of order of 10^33 cm^-2s^-1 is achievable for different options with
sqrt(s)_mu-p from 4.58 TeV to 12.7 TeV. Certainly, proposed mu-p colliders have
a huge potential for clarifying QCD basics and searches for new physics.
