Abstract: Heat-radiating substrate material characterized by a matrix of Ni-Fe alloy or Ni-Co-Fe alloy where a plurality of Cu elements penetrating cross-sectionally and the metals being mutually bonded by diffusion bonding to form multiple-core material.A method of manufacturing multiple-core complex material including process steps of manufacturing clad complex core member with a circular cross section, followed by formation of multiple-core complex billets composed of a plurality of complex core members filled in a metallic tube within the extent that the ratio of the inner diameter (D) of the metallic tube to the outer diameter (d) of the core member D/d is not less than 12, and then, after heating the complex billets, the core members are diffused and bonded together by a hot working at a reduction of area being not less than 20%.