A hot-forged TiAl-based alloy having excellent oxidation resistance and high strength at high temperatures, and a process for producing such an alloy. A TiAl-based alloy comprising Al: (40+a) atomic % and Nb: b atomic %, with the remainder being Ti and unavoidable impurities, wherein a and b satisfy formulas (1) and (2) below.
0≦a≦2 (1)
3+a≦b≦7+a (2)
Also, a TiAl-based alloy comprising Al: (40+a) atomic % and Nb: b atomic %, and further comprising one or more elements selected from the group consisting of V: c atomic %, Cr: d atomic % and Mo: e atomic %, with the remainder being Ti and unavoidable impurities, wherein a to e satisfy formulas (3) to (9) shown below.
0≦a≦2 (3)
3+a≦b+1.0c+1.8d+3.8e≦7+a (4)
b≧2 (5)
c≧0 (6)
d≧0 (7)
e≧0 (8)
c+d+e>0 (9)