The biepitaxial YBa2Cu3O7- x(YBCO)/CeO2/MgO Josephson junctions and c-axis YBCO/Au/Pb junctions have been fabricated to investigate the pairing state in YBCO. As a result, for the in-plane biepitaxial YBCO grain boundary junctions, both the integral and half-integral Shapiro steps are observed under zero applied magnetic field, suggesting the possibility of d-wave pairing in YBCO. On the other hand, Josephson tunneling currents have been observed on the YBCO/Au/Pb junctions with tunneling along the c axis of the YBCO films. The dependence of the Josephson critical current on the applied field for the YBCO/Au/Pb junctions exhibits an unconventional diffraction pattern which is close to the characteristic of a predominantly d-wave superconductor. The results are discussed in terms of the existing s-wave and d-wave symmetry theories.