An electro-conductive bonding material (20,30) includes: high-melting-point metal particles with a component having a first melting point, middle-melting-point metal particles having a second melting point, lower than the first melting point, low-melting-point metal particles having a third melting point, lower than the second melting point and preferably a flux. The high-melting-point metal particles include Au, Ag, Cu, Au-plated Cu, Sn-Bi-plated Cu and Ag-plated Cu particles. The middle-melting-point metal particles include Sn-Bi and Sn-Bi-Ag particles. The low-melting-point metal particles include Sn-Bi-ln and Sn-Bi-Ga particles. The electro-conductive bonding material (20,30) is used for bonding a substrate (6) and an electronic component (8). A method for bonding comprises supplying the electro-conductive bonding material (e.g. by paste printing) to any one of an electrode (7) of a substrate (6) and a terminal of an electronic component (8) (e.g. an Au bump (9)), heating the supplied electro-conductive bonding material at a temperature lower than the melting point of the middle-melting-point metal particles to form a first metallic bonding state, arranging the electronic component (8) on the substrate (6) with the electro-conductive bonding material in the first metallic bonding state therebetween and heating the electro-conductive bonding material at a temperature of the melting point of the middle-melting-point metal particles or higher and not exceeding 150 DEG C to convert the first metallic bonding state into a second metallic bonding state with a melting point of 250 DEG C or higher and form a bond.