  We present the general expressions for the resummation, up to next-to-leading
logarithmic accuracy, of Sudakov-type logarithms in processes with an
arbirtrary number of hard-scattering partons. These results document the
formulae used by the authors in several previous phenomenological studies. The
resummation formulae presented here, which are valid for phase-space
factorizable observables, determine the resummation correction in a
process-independent fashion. All process dependence is encoded in the colour
and flavour structure of the leading order and virtual one-loop amplitudes, and
in Sudakov weights associated to the cross section kinematics. We explicitly
illustrate the application to the case of Drell--Yan and prompt-photon
production.
