The reaction e + p → γ + jet + X is studied in QCD at the next-to-leading order. Previous studies on inclusive distributions showed good agreement with ZEUS data. To obtain a finer understanding of the dynamics of the reaction, several correlation functions are evaluated for ZEUS kinematics.This note is the continuation of the study of the deep inelastic scattering (DIS) reaction e + p → γ + jet + X with a photon and a jet in the final state. In a preceding paper [1] we calculated the next-to-leading order (NLO) QCD cross sections describing the photoproduction of a large-p ⊥ photon ( p γ ⊥ , η γ ) accompanied by a jet. In particular, we calculated the transverse momentum and rapidity distributions of the photon with the jet constrained in a given large range as well as the jet transverse momentum spectrum in events with a detected photon. In the present note we concentrate on the distributions in the following correlation variables:p ) (in the laboratory frame E e , E p are respectively the incident energies of the electron and the proton and y is the DIS inelasticity), η = η γ − η jet and φ = φ electron −φ γ . Note thatx p , as defined above, does not correspond to x p , the fraction of momentum carried by a parton in the proton, since we are not in a collinear frame. The correlations should provide a finer understanding of the underlying production mechanism than the inclusive cross sections.Originally the NLO calculation [2,3] was performed in the γ * − p center of mass (γ * is the virtual photon) in which a large scale is provided by a large value of p * γ ⊥ , the final γ transverse momentum in that frame. Production cross sections of hadrons and jets were studied in this frame and successfully described by the NLO calculation [4][5][6]. On the other hand, in the ZEUS experiment [7] the reaction e + p → γ + jet + X is studied in the laboratory frame for a