The neutron-rich nuclei ¹³⁶Sn and ¹³²Cd have been studied in the purpose of nuclear structure for the nuclei beyond the doubly-magic nucleus ¹³²Sn. The 2⁺₁ → 0⁺ _gs transitions were identified for these two nuclei using in-beam γ-ray spectroscopy in coincidence with one- and two-proton removal reactions, respectively, at the RIKEN Radioactive Isotope Beam Factory. The 2⁺ ₁ state in ¹³⁶Sn is found to be similar to that for ¹³⁴Sn indicating the seniority scheme may also hold for the heavy tin isotopes beyond N = 82. For ¹³²Cd, the 2⁺ ₁ state provides the first spectroscopic information in the even-even nuclei locating in the region “southeast” of ¹³²Sn and the result is discussed in terms of proton-neutron configuration mixing. In both these two nuclei, it was found that the valence neutrons play an essential role in their low-lying excitations.