A fine carbon fiber mixture produced through a vapor-growth process, which comprises fine carbon fiber, each fiber filament of the fiber having an outer diameter of 1 to 500 nm and an aspect ratio of 10 to 15,000 and comprising a hollow space extending along its center axis and a multi-layer sheath structure consisting of a plurality of carbon layers; and non-fibrous carbon such as flake-like carbon, granular carbon, or sheet-like carbon. A composition comprising a resin or a rubber and a fine carbon fiber mixture as above contained therein. An electrically conductive article or a sliding article comprising the composition.