The present invention relates to an adhesive composition applicable to skin comprising: (i) a polar oil or fat including (a) at least one triglyceride and/or (b) at least one fatty acid of the formula R-CO2H, wherein R is a C3 to C30 alkyl group; and (ii) at least one homopolymer, and/or copolymer. This invention also relates to a medical adhesive device including such adhesive composition.