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We investigate the prompt photon production in deep inelastic scattering at HERA in the framework of kT -factorization QCD approach. Our study is based on the off-shell partonic process eq --> eγq, where the photon radiation from the leptons as well as from the quarks is taken into account. The unintegrated quark densities in a proton are determined using the Kimber-Martin-Ryskin prescription. We investigate both inclusive and jet associated prompt photon productionrates. Our predictions are compared with the recent experimental data taken by the H1 and ZEUS collaborations.