  We generalize the Milne quantization condition to non-Hermitian systems. In
the general case the underlying nonlinear Ermakov-Milne-Pinney equation needs
to be replaced by a nonlinear integral differential equation. However, when the
system is PT-symmetric or/and quasi/pseudo-Hermitian the equations simplify and
one may employ the original energy integral to determine its quantization. We
illustrate the working of the general framework with the Swanson model and two
explicit examples for pairs of supersymmetric Hamiltonians. In one case both
partner Hamiltonians are Hermitian and in the other a Hermitian Hamiltonian is
paired by a Darboux transformation to a non-Hermitian one.
