Marco Marletta and Roman Romanov Absence of the absolutely continuous spectrum of a first-order non-selfadjoint Dirac-like system for slowly decaying perturbations (46K, LaTeX) ABSTRACT. We prove that the absolutely continuous subspace of the completely non-selfadjoint part of a first-order dissipative Dirac-like system is trivial when the imaginary part of the potential is non-integrable.