A chromatographic separation process for recovering a polyunsaturated fatty acid (PUFA) product from a feed mixture, which process comprises the steps of: (i) purifying the feed mixture in a first separation step in a simulated or actual moving bed chromatography apparatus having a plurality of linked chromatography columns containing, as eluent, an aqueous organic solvent, to obtain an intermediate product; and (ii) purifying the intermediate product obtained in (i) in a second separation step using a simulated or actual moving bed chromatography apparatus having a plurality of linked chromatography columns containing, as eluent, an aqueous organic solvent, to obtain the PUFA product; wherein (a) the first and second separation steps are carried out sequentially on the same chromatography apparatus, the intermediate product being recovered between the first and second separation steps and the process conditions in the chromatography apparatus being adjusted between the first and second separation steps such that the PUFA product is separated from different components of the feed mixture in each separation step; or (b) the first and second separation steps are carried out on separate first and second chromatography apparatuses respectively, the intermediate product being recovered from the first separation step and introduced into the second chromatography apparatus, and the PUFA product being separated from different components of the feed mixture in each separation step, and wherein the aqueous organic solvent eluent used in each separation step has a different water:organic solvent volume ratio; and wherein the intermediate product is collected as the raffinate stream in the first separation step, and the PUFA product is collected as the extract stream in the second separation step; or the intermediate product is collected as the extract stream in the first separation step, and the PUFA product is collected as the raffinate stream in the second separation step. (i) purifying the feed mixture in a first separation step in a simulated or actual moving bed chromatography apparatus having a plurality of linked chromatography columns containing, as eluent, an aqueous organic solvent, to obtain an intermediate product; and (ii) purifying the intermediate product obtained in (i) in a second separation step using a simulated or actual moving bed chromatography apparatus having a plurality of linked chromatography columns containing, as eluent, an aqueous organic solvent, to obtain the PUFA product; wherein (a) the first and second separation steps are carried out sequentially on the same chromatography apparatus, the intermediate product being recovered between the first and second separation steps and the process conditions in the chromatography apparatus being adjusted between the first and second separation steps such that the PUFA product is separated from different components of the feed mixture in each separation step; or (b) the first and second separation steps are carried out on separate first and second chromatography apparatuses respectively, the intermediate product being recovered from the first separation step and introduced into the second chromatography apparatus, and the PUFA product being separated from different components of the feed mixture in each separation step, and wherein the aqueous organic solvent eluent used in each separation step has a different water:organic solvent volume ratio; and wherein the intermediate product is collected as the raffinate stream in the first separation step, and the PUFA product is collected as the extract stream in the second separation step; or the intermediate product is collected as the extract stream in the first separation step, and the PUFA product is collected as the raffinate stream in the second separation step. (a) the first and second separation steps are carried out sequentially on the same chromatography apparatus, the intermediate product being recovered between the first and second separation steps and the process conditions in the chromatography apparatus being adjusted between the first and second separation steps such that the PUFA product is separated from different components of the feed mixture in each separation step; or (b) the first and second separation steps are carried out on separate first and second chromatography apparatuses respectively, the intermediate product being recovered from the first separation step and introduced into the second chromatography apparatus, and the PUFA product being separated from different components of the feed mixture in each separation step, and wherein the aqueous organic solvent eluent used in each separation step has a different water:organic solvent volume ratio; and wherein the intermediate product is collected as the raffinate stream in the first separation step, and the PUFA product is collected as the extract stream in the second separation step; or the intermediate product is collected as the extract stream in the first separation step, and the PUFA product is collected as the raffinate stream in the second separation step. wherein the intermediate product is collected as the raffinate stream in the first separation step, and the PUFA product is collected as the extract stream in the second separation step; or the intermediate product is collected as the extract stream in the first separation step, and the PUFA product is collected as the raffinate stream in the second separation step.