Following the recently observed empirical rule, two new high-temperature superconducting homologous series of the Ba-Ca-Cu-0 system have been discovered by using the high pressure synthesis technique: the interstitially doped Ba2Can-1CunO2n+2[02(n-1) n] for n = 3 and 4, and the CaBa2Can-1CunO2n+3[Ca-12(n-1) n] for n = 3. The 14-symmetric 02(n-1)n shows a Tc up to 126 K, the highest for superconductors without any volatile toxie elements, and degrades to a lower Tc compound when exposed to air; whereas the P4-symmetric Ca-12(n-1)n displays a Tc not to exceed 107 K and remains stable in air. More superconducting phases with a Tc up to 120 K have been detected in the Ba-Ca-G-0 system, although their structures have yet to be determined. These cornpounds provide excellent opportunities for the study of the role of charge-reservoir in high-temperature superconductivity, and the effects of symmetry on T, and structural instability. They may also be good material candidates for high-temperature superconducting thin-film devices operable above 120 K.