A heat-resistant austenitic alloy which contains 0.02-0.15%, excluding 0.02%, C, up to 2% Si, up to 3% Mn, up to 0.03% P, up to 0.01% S, 28-38% Cr, 40-60%, excluding 40%, Ni, up to 20% (including 0%) Co, 3-15%, excluding 3%, W, 0.05-1.0% Ti, 0.005-0.2% Zr, and 0.01-0.3% Al and has a N content up to 0.02% and a Mo content less than 0.5%, with the remainder being iron and impurities, and which satisfies relationships (1) to (3). The alloy has a high creep rupture strength, has satisfactory toughness even when used at a high temperature over long, and has excellent hot workability. This heat-resistant austenitic alloy may contain a specific amount of one or more elements selected from Nb, V, Hf, B, Mg, Ca, Y, La, Ce, Nd, Sc, Ta, Re, Ir, Pd, Pt, and Ag. P<=3 / {200(Ti+8.5Zr)} (1) 1.35Cr<=Ni+Co<=1.85Cr (2) Al>=1.5Zr (3).