The transition metal dichalcogenides provide a rich field for the study of two-dimensional materials, with metals, semiconductors, superconductors and charge density wave materials being known. Members of this family are typically hexagonal, but those based on rhenium (ReSe 2 and ReS 2 ) and their ternary alloys are attracting attention due to their triclinic structure and their resulting, strong in-plane anisotropy. Here, Raman spectra of dilute ReSe 2 -x S x alloys containing low levels of sulfur (x ≤ 0.25) were obtained in order to investigate the distribution of substitutional sulfur atoms over the non-equivalent chalcogen sites of the ReSe 2 unit cell. Four different Raman bands arising from the local vibrational modes of sulfur atoms were observed, corresponding to these four sites. One local vibrational mode has a substantially in-plane displacement of the sulfur atom, two are partially out-of-plane and one is completely out-of-plane. The interpretation of the experimental data is based on calculations of the lattice dynamics and nonresonant Raman tensors of a model alloy via density functional theory. For comparison, polarization-dependent Raman spectra of pure ReS 2 are also presented; a dramatic increase in the Raman cross-section is found for the out-of-plane modes when the excitation polarization is normal to the layers and the light propagates in the layer plane. A similar increase in cross-section is found experimentally for the local vibrational modes of sulfur in dilute ReSe 2 -x S x alloys and is predicted for dilute sulfur-containing alloys based on MoSe 2 . The analogous local vibrational modes of substitutional oxygen impurities in ReSe 2 were also investigated computationally.