The invention relates to the use of a detergent composition for removing hydrophobic residues and pigments on manufacturing or packaging devices or any other hardware used for manufacturing or packaging cosmetic or pharmaceutical compositions, said detergent composition including: a non-ionic surfactant selected from among the alkoxylated fatty alcohols; a non-aromatic co-surfactant selected from among the amine oxides, alkyl sulfates and alkyl sulfonates; and an organic alkaline agent selected from among the amino alcohols, excluding monoethanolamine, the non-aromatic co-surfactant being contained in the detergent composition in an amount of from 1 to 15 wt % in relation to the total weight of the composition.