**Talk will take place in Maths 513**

We generalize Weinberg's effective field theory approach to multiple-field inflation. In addition to standard terms in the Lagrangian we consider terms containing up to the fourth derivative of the scalar fields and the metric. The results illustrate the possible shapes of the interactions which will yield non-Gaussianity. Generally we find that the speed of sound differs from, but is close to unity, however large non-Gaussianities are possible in the multi-field case. The non-Gaussianity of the adiabatic mode and the entropy mode are correlated in shape and amplitude with the amount of the non-Gaussianity depending on the curvature of the classical field path in phase-space. We emphasize that in general the time derivative of adiabatic and entropy perturbations do not invariant due to the shift symmetry. However we find two specific combinations of them are invariant under such a symmetry and these combinations should be employed to construct an effective field theory of multi-field inflation.