A heat-resistant steel contains 0.1-3 mass % of Cr and satisfies the following equation: 0.1.ltoreq.Nb+Mo+V and MX-type complex precipitates formed inside microcrystalline grains contain 30 mass % or more of Mo and 7 mass % or more of Nb. Also provided is a process for producing the alloy steel product involving casting, forging, hot rolling, normalizing, optionally direct quenching, cooling at a predetermined cooling rate, and tempering.