We prove polynomial and exponential decay at infinity of eigen-vectors of partial differential operators related to radiation problems for time-harmonic generalized Maxwell systems in an exterior domain Ω⊂R ^N, N≥1, with non-smooth inhomogeneous, anisotropic coefficients converging near infinity with a rate r ^-τ, τ>1, towards the identity. As a canonical application we show that the corresponding eigen-values do not accumulate and that by means of Eidus' limiting absorption principle a Fredholm alternative holds true.