In a process for producing a large single-crystal component or directionally solidified component made of a nickel-based superalloy, the component is first cast into shape in a known manner to form a microstructure comprising dendrites, and then solution annealing for homogenizing the cast microstructure of the component and two-stage precipitation heat treatment are carried out. In order to avoid chemical inhomogeneities and internal stresses caused thereby, a HIP process with a pressure of higher than 160 MPa is carried out following the solution annealing.