The adhesive composition of the invention comprises a thermoplastic resin, a radical polymerizing compound, a radical polymerization initiator and a radical polymerization regulator. According to the present invention it is possible to provide an adhesive composition, a circuit connecting material, a connection structure for a circuit member and a semiconductor device whereby curing treatment can be carried out with sufficient speed at low temperature, curing treatment can be carried out with a wide process margin, and adequately stable adhesive strength can be obtained.