  We extend the complete Mellin (CM) representation of Feynman amplitudes to
the non-commutative quantum field theories. This representation is a versatile
tool. It provides a quick proof of meromorphy of Feynman amplitudes in
parameters such as the dimension of space-time. In particular it paves the road
for the dimensional renormalization of these theories. This complete Mellin
representation also allows the study of asymptotic behavior under rescaling of
arbitrary subsets of external invariants of any Feynman amplitude.
