  We study induced modules of nonzero central charge with arbitrary
multiplicities over affine Lie algebras. For a given pseudo parabolic
subalgebra ${\mathcal P}$ of an affine Lie algebra ${\mathfrak G}$, our main
result establishes the equivalence between a certain category of ${\mathcal
P}$-induced ${\mathfrak G}$-modules and the category of weight ${\mathcal
P}$-modules with injective action of the central element of ${\mathfrak G}$. In
particular, the induction functor preserves irreducible modules. If ${\mathcal
P}$ is a parabolic subalgebra with a finite-dimensional Levi factor then it
defines a unique pseudo parabolic subalgebra ${\mathcal P}^{ps}$, ${\mathcal
P}\subset {\mathcal P}^{ps}$. The structure of ${\mathcal P}$-induced modules
in this case is fully determined by the structure of ${\mathcal
P}^{ps}$-induced modules. These results generalize similar reductions in
particular cases previously considered by V. Futorny, S. K\"onig, V. Mazorchuk
[Forum Math. 13 (2001), 641-661], B. Cox [Pacific J. Math. 165 (1994), 269-294]
and I. Dimitrov, V. Futorny, I. Penkov [Comm. Math. Phys. 250 (2004), 47-63].
