To obtain a composition for local use having stability, high permissiveness, good makeup removing properties and a good cleansing efficiency by including a specific oxyethylenated compound, acetylenediol and an amphiphlic compound in a medium.

This composition is obtained by including (A) one or more oxyethylenated acetylenediols represented by the formula (R and R' are each a 1-10C alkyl radical; n and m are each O-10) (preferably an oxyethylenated derivative of 2,4,7,9-tetramethyl-5-decyne-4,7-diol) in an amount of 0.01-0.5 wt.% based on the total amount of the composition and (B) preferably 0.001-10 wt.% of at least one preferably nonionic amphiphlic compound (preferably an alkoxylated or a glycerolated alkenyl succiniate) having ≥15 HLB in order to dissolve the ingredient A in a physiologically acceptable medium.