Modulation of the dynamic resistance versus the magnetic field of YBa2Cu3O7-δ single crystal shows two groups of peak structures with nearly uniform magnetic field spacings. The spacings suggest two kinds of Josephson junctions: one formed by the CuO2-Y-CuO2 atomic planes within each unit cell and the other formed by the CuO2 bilayers between different unit cells. The intra-unit-cell junctions appear first as the temperature is lowered from Tc. The existence of CuO2-Y-CuO2 Josephson junctions implies two-dimensional superconductivity in the CuO2 atomic planes.