  Let g_A (respectively, g_A(\mu)) be the graded multi-loop Lie algebra
(respectively graded twisted multi-loop Lie algebra)" associated with the
simple finite dimensional Lie algebra g over the complex field C. In this
paper, we prove that irreducible integrable g_A(\mu)-modules with finite
dimensional weight spaces are either highest weight modules or their duals and
classify the isomorphism classes of irreducible integrable g_A-modules and
g_A(\mu)-modules with finite dimensional weight spaces.
