To provide an adhesive composition high in initial adhesion rate, excellent in formability of a coating film in winter, low in temperature dependence of viscosity, high in modules of a dried coating film and further excellent in water resistance and a paper tube high in strength under pressure.

An adhesive composition comprises, as the major component, an ethylene-vinyl acetate copolymer resin emulsion to be obtained by the emulsion polymerization of a monomer composed of 85-95 wt.% vinyl acetate and 5-15 wt.% ethylene in the presence of a modified polyvinyl alcohol-based polymer containing 1-10 mol.% α-olefin units having not more than 4 carbon atoms in the molecule. In a paper tube to be obtained by winding paper tube stock paper in layers in the shape of a tube, the adhesion of the paper tube stock paper is done with said adhesive composition.