Olefin block copolymers (A-1) are disclosed represented by the formula (I) PO.sup.1-g.sup.1-B.sup.1 . . . (I) wherein PO.sup.1 is a segment comprised of repeating units derived from an olefin having 2 to 20 carbon atoms, g.sup.1 is an ester, ether, amide, imide, urethane, urea, silylether or carbonyl linkage, and B.sup.1 is a segment containing an unsaturated hydrocarbon or a hetero atom. The olefin block copolymers are suitable for uses in adhesives, various molded articles such as construction and civil engineering materials, automobile interior and exterior materials, gasoline tanks, electric and electronic parts, medical care and sanitation materials, materials of miscellaneous goods, resin materials having environmental degradation properties, films and sheets, modifiers and dispersions.