The application of high nearly hydrostatic pressures at elevated temperatures on the LEK94 single crystal (SX) nickel-based superalloy directly affects its microstructure. This is due to a combination of the effect of pressure on the Gibbs free energy, on the diffusion coefficients of the alloying elements, on the internal coherent stresses, and on the porosity distribution. The last effect depends at least on the first three. Therefore, based on the theoretical influences of the pressure, the main objective of this work is to understand, by means of an experimental work, the effect of high pressure at elevated temperature during annealing on the evolution of the phases morphology, and porosity of the high-temperature material LEK94. Specifically, pressures up to 4 GPa, temperatures up to 1180 A degrees C, and holding times up to 100 h were investigated. The main findings are that, porosity can be considerably reduced without affecting significantly the gamma/gamma' microstructure by high pressure annealing and the verification that increasing the external pressure stabilizes the gamma'-phase.