  We present the construction of unintegrated double parton distribution
functions which include dependence on transverse momenta of partons. We extend
the formulation which was used to obtain the single unintegrated parton
distributions from the standard, integrated parton distribution functions.
Starting from the homogeneous part of the evolution equations for the
integrated double parton distributions, we construct the unintegrated double
parton distributions as the convolutions of the integrated double distributions
and the splitting functions, multiplied by the Sudakov form factors. We show
that there exist three domains of external hard scales which require three
distinct forms of the unintegrated double distributions. The additional
transverse momentum dependence which arises through the Sudakov form factors
leads to non-trivial correlations in the parton momenta. We also discuss the
non-homogeneous contribution to the unintegrated double parton distributions,
which arises due to the splitting of a single parton into daughter partons with
high transverse momenta. We analyze two cases, the unfolding of the transverse
momenta dependence from the last step of the evolution of two partons, and the
case where the transverse momenta are generated directly from the single parton
splitting.
