BiPd2O4 and PbPd2O4 were synthesized at high pressure of 6 GPa and 1500 K. Crystal structures of BiPd2O4 and PbPd2O4 were studied with synchrotron X-ray powder diffraction. BiPd2O4 is isostructural with PbPt2O4 and crystallizes in a triclinic system (space group P (1) over bar, a = 5.73632(4) angstrom, b = 6.02532(5) angstrom, c = 6.41100(5) angstrom, alpha = 114.371(1)degrees, beta = 95.910(1)degrees, and gamma = 111.540(1)degrees at 293 K). PbPd2O0 is isostructural with LaPd2O4 and BaAu2O4 and crystallizes in a tetragonal system (space group I4(1)/a, a = 5.76232(1) angstrom, and c = 9.98347(2) angstrom at 293 K). BiPd2O4 shows ordering of Pd2+ and Pd4+ ions, and it is the third example of compounds with ordered arrangements of Pd2+ and Pd4+ in addition to Ba2Hg3Pd7O4 and KPd2O3. In PbPd2O4, the following charge distribution is realized Pb4+Pd22+O4. PbPd2O4 shows a structural phase transition from I4(1)/a to I2/a at about 240 K keeping basically the same structural arrangements (space group I2/a, a = 5.77326(1) angstrom, b = 9.95633(2) angstrom, c = 5.73264(1) angstrom, beta = 90.2185(2)degrees at 112 K). BiPd2O4 is nonmagnetic while PbPd2O4 exhibits a significant temperature-dependent paramagnetic moment of 0.46 mu(B)/f.u. between 2 and 350 K. PbPd2O4 shows metallic conductivity, and BiPd2O4 is a semiconductor between 2 and 400 K.