Solid, shaped and fired fibers of Ti.sub.4O.sub.7 and Ti.sub.5O.sub.9 are made by firing TiO.sub.2 fibers in a reducing atmosphere. In a first aspect, the TiO.sub.2 fibers are made by extruding into air a viscous TiO.sub.2 gel and heat treating the resulting green fibers to remove solvent, decompose and to volatilize undesired constituents to form electrically conductive, refractory fibers of Ti.sub.4O.sub.7 and Ti.sub.5O.sub.9. In a second aspect, solid, shaped and fired fibers of Ti.sub.4O.sub.7 and Ti.sub.5O.sub.9 are made by firing extruded fibers from mixtures of TiO.sub.2.