Cosmetic or dermatological oil-in-water emulsion composition comprising, in a physiologically acceptable medium, at least one dimeric surfactant of formula (I): ** (See formula) ** in which: - R1 and R3 independently designate from each other, an alkyl radical having 1 to 25 carbon atoms； - R2 designates a spacer consisting of a linear or branched alkylene chain having 1 to 12 carbon atoms； - X and Y designate, independently of each other, a group - (C2H4O) a- (C3H6O) bZ where * Z designates a hydrogen atom or a radical -CH2-COOM, -SO3M, -P (O) (OM )2； -C2H4-SO3M, -C3H6- SO3M or -CH2 (CHOH) 4CH2OH, where M represents H or an alkaline or alkaline earth or ammonium or alkanolammonium ion, * a goes from 0 to 15, * b goes from 0 to 10, and * the sum of a + b ranges from 1 to 25； and - n ranges from 1 to 10, in association with an effective amount of at least one solid semicrystalline polymer at room temperature and with a melting temperature below 70 ° C, comprising a) a polymeric skeleton and b) at least one crystallizable organic side chain and / or a crystallizable organic sequence that is part of the skeleton of said polymer, said polymer having a number average molecular mass greater than or equal to 2000, said semicrystalline polymer being chosen from among the homopolymers and copolymers resulting from the polymerization of at least one crystallizable chain monomer chosen from among the C14-C24 saturated (meth) alkyl acrylates； wherein said emulsion has a fat phase index greater than 10% by weight with respect to the total weight of said composition and comprises more than 40% by weight of non-volatile oil (s) with respect to the weight of said fat phase； where said composition is different from the following compositions A and B: ** (See table) **Composición cosmética o dermatológica de tipo emulsión aceite en agua que comprende, en un medio fisiológicamente aceptable, al menos un tensioactivo di mérico de fórmula (I): **(Ver fórmula)** en la cual: - R1 y R3 des
