  Different limitations on luminosity of linac-ring type colliders coming from
beam dynamics issues are considered for the examples of the $ep$ options of the
THERA and LinacXLHC proposals. It is shown that $L=1.3\times 10^{31}$ for THERA
and $L=2.7\times 10^{32}$ for LinacXLHC can be achieved for round beams case.
Corresponding sets of parameters are given with the explanations.
