The present invention relates to a kit for coating a nail or false nail, and more particularly for making up a nail or false nail, comprising: - a first photo-crosslinkable cosmetic composition comprising, in a physiologically acceptable medium, at least one photo-crosslinkable compound a) corresponding to formula (I) in which formula (I) - R1, R2 and R3, which may be identical or different, represent a hydrogen atom or a C1-C10 alkyl group, n represents an integer between 1 and 10, - the bond between α and β of the carbonyloxy is a single bond or a double bond or is a bond included in a (hetero)cycle comprising from 5 to 7 carbon atoms and - a second photo-crosslinkable composition comprising, in a physiologically acceptable medium: • at least one photo-crosslinkable compound b) comprising at least one (poly)urethane poly(ALK)acrylate compound comprising a (poly)oxyalkylene unit, • at least one photo-crosslinkable compound c) comprising at least two carbamate units obtained by reaction with at least one diisocyanate of isophorone diisocyanate type, • at least one (ALK)acrylate monomer, preferably (meth)acrylate monomer, more preferentially tetrahydrofurfuryl methacrylate. The present invention also relates to specific methods for applying such a composition.
