We report on the atomic structure and electronic properties of self-organized dysprosium and erbium silicide nanowires on Si(557), studied using scanning tunneling microcopy and angle-resolved photoelectron spectroscopy. The nanowires were prepared by deposition of different rare earth amounts and subsequent annealing for silicide formation. Due to the stepped structure of the Si(557) surface, nanowires form along the step edges, showing a variety of structurally and electronically different types, depending on the preparation conditions. At submonolayer dysprosium coverages, different chainlike structures dominate, showing one-dimensional dispersion with half-metallic properties. These nanowire regions are separated by $7\ifmmode\times\else\texttimes\fi{}7$ reconstructed Si(111) facets or submonolayer dysprosium silicide patches on these facets. At monolayer coverages, in contrast, mainly nanowires with lengths exceeding $1\text{ }\ensuremath{\mu}\text{m}$ and widths of a few nanometers are found, forming on the (111) facets of the Si(557) surface. Their electronic properties are characterized by a two-dimensional band structure with strong dispersion both parallel and perpendicular to the nanowires and clear metallic behavior, and it is demonstrated that they are formed from hexagonal ${\text{DySi}}_{2}$ monolayers. In the case of thicker silicide layers, metallic nanowires form again on the Si(111) facets, but with clear structural and electronic characteristics of hexagonal ${\text{Dy}}_{3}{\text{Si}}_{5}$ multilayers. At these coverages, additional structures are found, which show an intense signal in the photoelectron spectroscopy data. Related experiments on the growth of erbium silicides indicated the formation of very similar nanowire structures.