  We propose a matrix evolution equation in (x,kt)-space for flavour singlet,
unintegrated quark and gluon densities, which generalizes DGLAP and BFKL
equations in the relevant limits. The matrix evolution kernel is constructed so
as to satisfy renormalization group constraints in both the ordered and
antiordered regions of exchanged momenta kt, and incorporates the known NLO
anomalous dimensions in the MSbar scheme as well as the NLx BFKL kernel. We
provide a hard Pomeron exponent and effective eigenvalue functions that include
the n_f-dependence, and give also the matrix of resummed DGLAP splitting
functions. The results connect smoothly with those of the single-channel
approach. The novel P_{qa} splitting functions show resummation effects delayed
down to x=0.0001, while both P_{ga} entries show a shallow dip around x=0.001,
similarly to the gluon-gluon single-channel results. We remark that the matrix
formulation poses further constraints on the consistency of a BFKL framework
with the MSbar scheme, which are satisfied at NLO, but marginally violated by
small n_f/N_c^2-suppressed terms at NNLO.
