  We study the non-gaussianity from the bispectrum in multi-field inflation
models with a general kinetic term. The models include the multi-field
K-inflation and the multi-field Dirac-Born-Infeld (DBI) inflation as special
cases. We find that, in general, the sound speeds for the adiabatic and entropy
perturbations are different and they can be smaller than 1. Then the
non-gaussianity can be enhanced. The multi-field DBI-inflation is shown to be a
special case where both sound speeds are the same due to a special form of the
kinetic term. We derive the exact second and third order actions including
metric perturbations. In the small sound speed limit and at leading order in
the slow-roll expansion, we derive the three point function for the curvature
perturbation which depends on both adiabatic and entropy perturbations. The
contribution from the entropy perturbations has a different momentum dependence
if the sound speed for the entropy perturbations is different from the
adiabatic one, which provides a possibility to distinguish the multi-field
models from single field models. On the other hand, in the multi-field DBI
case, the contribution from the entropy perturbations has the same momentum
dependence as the pure adiabatic contributions and it only changes the
amplitude of the three point function. This could help to ease the constraints
on the DBI-inflation models.
