The twelve quaternary rare-earth selenides Ba(2)MLnSe(5) (M = Ga, In; Ln = Y, Nd, Sm, Gd, Dy, Er) have been synthesized for the first time. The compounds Ba(2)GaLnSe(5) (Ln = Y, Nd, Sm, Gd, Dy, Er) are isostructural and crystallize in a new structure type in the centrosymmetric space group P (1) over bar of the triclinic system while the isostructural compounds Ba(2)InLnSe(5) (Ln = Y, Nd, Sm, Gd, Dy, Er) belong to the Ba2BiInS5 structure type and crystallize in the noncentrosymmetric space group Cmc2(1) of the orthorhombic system. The structures contain infinite one-dimensional anionic chains (infinity)1[GaLnSe(5)](4-) and (infinity)1[InLnSe(5)](4-), and both chains are built from LnSe(6) octahedra and MSe4 (M = Ga, In) tetrahedra in the corresponding selenides. As deduced from the diffuse reflectance spectra, the band gaps of most Ba(2)MLnSe(5) (M = Ga, In; Ln = Y, Nd, Sm, Gd, Dy, Er) compounds are around 2.2 eV. The magnetic susceptibility measurements on Ba2GaGdSe5 and Ba(2)InLnSe(5) (Ln = Nd, Gd, Dy, Er) indicate that they are paramagnetic and obey the Curie-Weiss law, while the magnetic susceptibility of Ba2InSmSe5 deviates from the Curie-Weiss law as a result of the crystal field splitting. Furthermore, Ba2InYSe5 exhibits a strong second harmonic generation response close to that of AgGaSe2, when probed with the 2090 nm laser as fundamental wavelength.