A circuit-connecting material interposed between mutually-facing circuit electrodes, and electrically connecting the electrodes, either by direct contact, or via conductive particles present in the material. The circuit-connecting material features: (1) a curing agent capable of generating free radicals upon heating; (2) a radical-polymerizable substance, and two or more microscopically separated phases. The two or more microscopically separated phases include an elastomer phase of carboxyl-group-containing elastomer and a phenoxy resin phase of a phenoxy resin having a weight average molecular weight of 10,000 or more.