  We discuss issues related to the resummation of non-global observables in
QCD, those that are sensitive to radiation in only a part of phase space.
Examples of such observables are certain single-hemisphere event shapes in e+e-
and DIS. Compared to global observables (those sensitive to all emissions, e.g.
the e+e- thrust) a new class of single-logarithmic terms arises. These have
been neglected in recent calculations in the literature. For a whole set of
single hemisphere e+e- and DIS event shapes, we analytically evaluate the first
such term, at order alpha_s^2, and give numerical results for the resummation
of these terms in the large-Nc limit.
