We prove a functional central limit theorem for the empirical process of a stationary process X t =Y t +V t , where Y t is a long memory moving average in i.i.d. r.v.’s ζ s , s ≤ t, and V t =V (ζ t , ζ t-1,...) is a weakly dependent nonlinear Bernoulli shift. Conditions of weak dependence of V t are written in terms of L 2-norms of shift-cut differences V (ζ t , ζ t-n , 0,...,) − V(ζ t ,...,ζ t-n+1, 0,...). Examples of Bernoulli shifts are discussed. The limit empirical process is a degenerated process of the form f(x)Z, where f is the marginal p.d.f. of X 0 and Z is a standard normal r.v. The proof is based on a uniform reduction principle for the empirical process.