The invention relates to a composition for inhibiting corrosion of the upper part (or roof) of a pipeline for conveying wet hydrocarbons, i.e. hydrocarbons comprising a variable amount of water, said composition comprising at least one Amine 1 with vapor pressure greater than or equal to 10 mmHg, and at least one. Amine 2 with vapor pressure greater than or equal to 0.1 mmHg and strictly less than 10 mmHg.The invention also relates to the use of such a composition, and also to the method of inhibiting top-of-line corrosion employing said inhibitor composition.