A process for separating hydrocarbons from an LNG, including the steps of: distilling a feed LNG in a first distillation column to separate it into a fraction enriched with methane and a fraction enriched with components heavier than methane; distilling the fraction enriched with components heavier than methane in a second distillation column to separate it into a fraction enriched with ethane and a fraction enriched with components heavier than ethane; recovering the cryogenic heat of the feed LNG to be fed into the first distillation column or of the liquid inside the first distillation column by using a heat transfer medium; and cooling the overhead gas of the second distillation column by using the heat transfer medium which has recovered the cryogenic heat to condense at least part of the overhead gas of the second distillation column. An apparatus for carrying out this process.