  We investigate the primordial non-Gaussianities from the trispectra in
multi-field inflation models, which can be seen as generalization of
multi-field $k$-inflation and multi-DBI inflation. We derive the full
fourth-order perturbation action for the inflaton fields and evaluate the
four-point correlation functions for the perturbations in the limit $\ca \ll 1$
and $\ce \ll1$. There are three types of momentum-dependent shape functions
which arise from three types of four-point interaction vertices. The final
trispectrum of the curvature perturbation can be expressed in terms of the
deformations and permutations of these three shape functions, and is determined
by $\ca$, $\ce$, $\lambda$, $\Pi$ which depend on the non-linear structure of
the model and also the transfer function $T_{\Rc\Sc}$. We also discuss the
parameter space for the trispectrum and plot the shape diagrams for the
trispectrum both for visualization and for distinguishing different shapes from
each other.
