A circuit terminal connected structure and a circuit terminal connecting method are provided. Both the structure and the method feature a circuit connecting material formulated with the following components: a curing agent capable of generating free radicals upon heating; an acrylate or methacrylate radical polymerizable substance; and either an acrylic rubber or a maleimide radical polymerizable substance having at least two maleimide groups per molecule. In some embodiments, the curing agent features a 10-hour half life temperature of 40° C. or above and a 1-minute half-life temperature of 180° C. or below. In other embodiments, the circuit connecting material includes conductive particles. In additional embodiments, the circuit connecting material includes a hydroxyl-group-containing resin having a weight average molecular weight of 10,000 or more.