An ester composition including at least 90% wt of the dialkyi ester of 2,5-furandicarboxylic acid as starting dialkyi ester concentration and up to 5% wt of the monoalkyi ester of 2,5-furandicarboxylic acid as starting monoalkyi ester concentration, the percentages being based on the weight of the ester composition, is purified in a process which includes subjecting the ester composition to melt crystallization to yield a purified dialkyi ester composition containing a dialkyi ester concentration higher than the starting dialkyi ester concentration and a melt residue containing a monoalkyi ester concentration higher than the starting monoalkyi ester concentration. From the melt residue a purified monoalkyi ester composition and a contaminants-rich residue can be prepared via melt crystallization. The purified dialkyi ester composition and/or the purified monoalkyi ester composition can be hydrolyzed to yield purified 2,5-furandicarboxylic acid.