Abstract: An Ni-based or Ni—Co-based heat-resistant alloy wire excellent in resistance to sag at high temperatures ranging from 600 to 700° C., which excellent resistance is most suitable for spring materials. The heat-resistant alloy wire contains (a) 0.01 to 0.40 wt % C, 5.0 to 25.0 wt % Cr, and 0.2 to 8.0 wt % Al; (b) at least one constituent selected from the group consisting of 1.0 to 18.0 wt % Mo, 0.5 to 15.0 wt % W, 0.5 to 5.0 wt % Nb, 1,0 to 10.0 wt % Ta, 0.1 to 5.0 wt % Ti and 0.001 to 0.05 wt % B; (c) at least one constituent selected from the group consisting of 3.0 to 20.0 wt % Fe and 1.0 to 30.0 wt % Co; and (d) the remaining constituent consisting mainly of Ni and unavoidable impurities. The wire has (a) a tensile strength not less than 1,400 N/mm2 and less than 1,800 N/mm2, (b) an average crystal-grain diameter not less than 5 &mgr;m and less than 50 &mgr;m in a cross section, and (c) a crystal-grain aspect ratio (a major-axis/minor-axis ratio) of 1.2 to 10 in a longitudinal section.