  We consider the singular behaviour of QCD scattering amplitudes in
kinematical configurations where two or more momenta of the external partons
become collinear. At the tree level, this behaviour is known to be controlled
by factorization formulae in which the singular collinear factor is universal
(process independent). We show that this strict (process-independent)
factorization is not valid at one-loop and higher-loop orders in the case of
the collinear limit in space-like regions (e.g., collinear radiation from
initial-state partons). We introduce a generalized version of all-order
collinear factorization, in which the space-like singular factors retain some
dependence on the momentum and colour charge of the non-collinear partons. We
present explicit results on one-loop and two-loop amplitudes for both the
two-parton and multiparton collinear limits. At the level of square amplitudes
and, more generally, cross sections in hadron--hadron collisions, the violation
of strict collinear factorization has implications on the non-abelian structure
of logarithmically-enhanced terms in perturbative calculations (starting from
the next-to-next-to-leading order) and on various factorization issues of mass
singularities (starting from the next-to-next-to-next-to-leading order).
