  In asymptotically free theories with collinear divergences it is sometimes
claimed that these divergences cancel if one sums over initial and final state
degenerate cross-sections and uses an off-shell renormalisation scheme. We show
for scalar $\phi^3$ theory in six dimensions that there are further classes of
soft collinear divergences and that they do not cancel. Furthermore, they yield
a non-convergent series of terms at a fixed order of perturbation theory.
Similar effects in gauge theories are also summarised.
