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The anisotropy of thermal conductivity k in single crystals YBa2Cu3O7 has been studied. The temperature dependence of k in c-direction is well described by the lattice thermal conductivity ( T max =60 K ; k max =4 W / mK ; T D =140 K ) . The precise measurements reveal the hysteretic behavior of out-of-plane thermal conductivity. In ab-direction the upturn in k for temperatures below Tc is observed and temperatures of thermal conductivity peaks in ab- and c-direction coincide. Theoretical analysis suggests a model in which an observed peak below Tc in thermal conductivity for ab-direction is ascribed to a quasiparticle contribution.