  We use transport techniques to calculate the trispectrum produced in
multiple-field inflationary models with canonical kinetic terms. Our method
allows the time evolution of the local trispectrum parameters, tauNL and gNL,
to be tracked throughout the inflationary phase. We illustrate our approach
using examples. We give a simplified method to calculate the superhorizon part
of the relation between field fluctuations on spatially flat hypersurfaces and
the curvature perturbation on uniform density slices, and obtain its
third-order part for the first time. We clarify how the 'backwards' formalism
of Yokoyama et al. relates to our analysis and other recent work. We supply
explicit formulae which enable each inflationary observable to be computed in
any canonical model of interest, using a suitable first-order ODE solver.
