  A systematic extension of the Monte Carlo (MC) algorithm, that solves the
DGLAP equation, into the so-called the one-loop CCFM evolution is presented.
Modifications are related to a z-dependent coupling constant; transverse
momentum dependence is added to the x-dependence of the parton distributions.
The presented Markovian algorithm for one-loop CCFM evolution is the first step
in extending it to other more sophisticated schemes beyond DGLAP. In
particular, implementing the complete CCFM will be the next step. The presently
implemented one-loop CCFM option will be a useful tool in testing the
forthcoming MC solutions. Numerical results of the new MC are confronted with
other non-MC numerical solutions. The agreement within the MC statistical error
of ~0.1% is found. Also, numerical results for kT-dependent structure functions
are presented.
