The present invention refers to new purified compositions of long chain polyunsaturated fatty acids, or their salts or esters, characterized by being essentially free from other usually present—but structurally different—components, such as furan fatty acids, phytanic and pristanic acids, squalene, and some oligomers, as well as several “persistent” environmental pollutants, such as polychlorinated dibenzo-dioxins and polychlorinated dibenzo-furans, polychlorinated biphenyls, polybrominated diphenyl-ethers, polycyclic aromatic hydrocarbons, and others, which are also usually present and extremely toxic. The invention also refers to the purification method to obtain said compositions and the use thereof as food, food for special medical use, food and diet supplement, and drug.