  We discuss the BFKL equation with a running gauge coupling and identify in
its solutions the contributions originating from different transverse momentum
scales. We show that for a running coupling constant the distribution of the
gluons making up the BFKL Pomeron shifts to smaller transverse momenta so that
the dominant part of Pomeron can have a nonperturbative origin. It is
demonstrated how this soft physics enters into the BFKL solution through the
boundary condition. We consider two kinematical regimes leading to different
behaviour of the rapidity and transverse momentum dependence of the gluon
distribution. In the diffusion approximation to the BFKL kernel with running
$\alpha_s$, we find a sequence of poles which replaces the cut for fixed
$\alpha_s$. The second regime corresponds to the singular part of the kernel,
which gives the dominant contribution in the limit of very large transverse
momenta. Finally, a simple more general picture is obtained for the QCD Pomeron
in hard processes: it is of soft, nonperturbative nature, but has hard ends of
DGLAP-type.
