  We discuss the large-x behaviour of the splitting functions P_qg and P_gq and
of flavour-singlet coefficient functions, such as the gluon contributions C_2,g
and C_L,g to the structure functions F_2,L, in massless perturbative QCD. These
quantities are suppressed by one or two powers of 1-x with respect to the
1/(1-x) terms which are the subject of the well-known threshold exponentiation.
We show that the double-logarithmic contributions to P_qg, P_gq and C_L at
order alpha_s^4 can be predicted from known third-order results and present, as
a first step towards a full all-order generalization, the leading-logarithmic
large-x behaviour of P_qg, P_gq and C_2,g at all orders in alpha_s.
