An electrical connecting device including a first circuit board providing thereon with input/output terminals, each of the terminals having a tip surface coated with gallium and a second circuit board providing thereon with contact terminals, each of the terminals having a tip surface coated with indium or tin. A low-melting point alloy layer is formed by a mutual action between gallium and indium or tin, when the input/output terminals of the first circuit board are in contact with the respective terminals of the second circuit board and electrically connected to each other. The second metal layer includes a plurality of wire-like metal supports extending substantially perpendicular to the surface of the terminal and a low-melting point metal retained by the wire-like metal supports.