  We investigate the next-to-leading logarithmic (NLL) order contributions of
the quantum chromodynamics (QCD) for exclusive processes evaluated by Monte
Carlo methods. Ambiguities of the Monte Carlo calculation based on the
leading-logarithmic (LL) order approximations are pointed out. To remove these
ambiguities, we take into account the NLL order terms.
  In a model presented in this paper, interference contributions due to the NLL
order terms are included for the generation of the transverse momenta in
initial-state parton radiations. Furthermore, a kinematical constraint due to
parton radiation, which is also a part of the NLL order contributions, is taken
into account. This method guarantees a proper phase space boundary for hard
scattering cross sections as well as parton radiations.
  As an example, cross sections for lepton pair productions mediated by a
virtual photon in hadron-hadron collisions are calculated, using the
jet-calculus scheme for flavor nonsinglet quarks.
