The present invention relates to a cosmetic composition containing a combination i) of at least one screening agent of the dibenzoylmethane derivative type and ii) of at least one particular hydrophilic or water-soluble merocyanin UV-screening agent, especially corresponding to one of the formulae (I) or (II) below: in which at least one or two of the radicals contain: either an alkylsulfonate radical in its acid or salified form or one or two hydroxyl radicals. The invention also relates to a process for the radiation-photostabilization of at least one screening agent of the dibenzoylmethane derivative type with an effective amount of at least one particular hydrophilic or water-soluble merocyanin UV-screening agent, especially corresponding to one of the formulae (I) or (II).