Topically applicable, fluid anti-sun/sunscreen compositions useful for protecting the skin and/or the hair against the damaging effects of ultraviolet radiation, contain:(a) at least one photoprotective system for screening out UV radiation; and(b) at least one tertiary-amide-terminated polyamide (ATPA) polymer, formulated into a topically applicable, cosmetically acceptable aqueous support therefor; the subject anti-sun/sunscreen compositions are especially provided as sprays, notably for the purpose of increasing the sun protection factor (SPF) and/or of reducing or even eliminating the fluffing effect thereof.