Near-stoichiometric compositions of Ba(B′1/3B″2/3)O3 (B′ = Mg, Co, or Zn and B″ = Nb or Ta) perovskite-type materials with nonstoichiometry on Ba and B′ positions were studied by room temperature Raman spectroscopy and transmission electron microscopy. The studied materials with 1:2 ratio of B-site cations belong to the family of perovskites that has tolerance factor larger than unity, indicating formation of a strained structure. This family of materials exhibits phase transition from a completely disordered phase having space group Pm-3m to a 1:2-ordered phase with space group P-3m1. Measured Raman spectra were attributed to the presence of 1:2-cation order and are characterized by the presence of seven modes, the strongest of which at 800 cm−1 originates from collective motion of oxygen octahedra. The appearance of a mode at 670 cm−1 in Co-containing samples was ascribed to the formation of a 1:1-ordered phase and was confirmed by selected-area electron diffraction.