  We consider the production of a colourless system at next-to-leading order in
the strong coupling constant $\alpha_s$. We impose a transverse-momentum
cutoff, qtcut, on the colourless final state and we compute the power
corrections for the inclusive cross section in the cutoff, up to the fourth
power.
  The study of the dependence of the cross section on qtcut allows for an
understanding of its behaviour at the boundaries of the phase space, giving
hints on the structure at all orders in $\alpha_s$ and on the identification of
universal patterns. The knowledge of such power corrections is also a required
ingredient in order to reduce the dependence on the transverse-momentum cutoff
of the QCD cross sections at higher orders, when the qt-subtraction method is
applied.
  We present analytic results for both Drell--Yan vector boson and Higgs boson
production in gluon fusion and we illustrate a process-independent procedure
for the calculation of the all-order power corrections in the cutoff. In order
to show the impact of the power-correction terms, we present selected numerical
results and discuss how the residual dependence on qtcut affects the total
cross section for Drell--Yan Z production and Higgs boson production via gluon
fusion at the LHC.
