We have synthesized the Hg-containing Barium-based cuprate of the HgBa2Ca2Cu3O8+delta (1223) compound with T-c up to 135 K without post-annealing by directly mixing from mono-oxide powders of Hg, Ba, Ca, and Cu as starting materials. This is the n = 3 phase of the homologous series HgBa2Can-1CunO2n+2+delta>. The isotopic strontium-based cuprates, corresponding to the formula HgSr2Can-1CunO2n+2+delta have not been synthesized up to now. However, the stabilization of the strontium cuprates with n = 1 and 2 structures can be performed by introducing a second element (e.g. Pb) besides Hg in the hole reservoir layers. Moreover, the chemical doping of Y3+ into the Ca2+ sites and La3+ into the Sr2+ sites in the strontium cuprates of the n = 1 and n = 2 compounds, respectively, is necessary to induce superconductivity. Bulk superconductivity with T-c up to 35 K and 90 K has been achieved in (Pb0.5Hg0.5)(Sr1.2La0.8)CuO4+delta (n = 1) and (Pb0.5Hg0.5)Sr-2(Ca0.7Y0.3)Cu2O6+delta (n = 2), respectively. The crystal structures of the newly discovered Hg-containing phases have been investigated by selected area electron diffraction (SAED). The appearance of superlattice spots with a commensurate modulation in the SAED patterns was observed in the Hg-containing Sr-based cuprates. However, such a phenomenon was not found in the HgBa2Ca2Cu3O8+delta phase.