Abstract: A process for recovering at least one of purified polyunsaturated fatty acids (PUFA) and polyunsaturated fatty acid mixtures from a feed composition includes a step of (i) treating the composition by either (a) stationary bed chromatography or (b) multistage countercurrent column fractionation in which a solvent is a fluid at supercritical pressure, and recovering at least one PUFA-enriched fraction. The process also includes a step of (ii) subjecting the fraction recovered in the treating step to further fractionation by simulated continuous countercurrent moving bed chromatography, and recovering at least one fraction containing the purified PUFA or the PUFA mixture.