Proof of factorization of soft and collinear divergences in non-equilibrium QCD may be necessary to study hadronic signatures of quark-gluon plasma at RHIC and LHC. In this paper we prove factorization of soft and collinear divergences in non-equilibrium QED by using Schwinger-Keldysh closed-time path integral formalism in the background field method in pure gauge. (C) 2009 Elsevier Inc. All rights reserved.