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We analyze the double polarization asymmetry of the ω-meson photoproduction in the vector-meson-dominance model of diffractive production and the one-pion exchange model. We find that the longitudinal beam-target asymmetry is very sensitive to the real part of the diffractive photoproduction amplitude and to the sign of the ωπγ coupling because of the different spin structures of the amplitudes associated with the different mechanisms.