Composition containing a nerve fiber reactivity modulating compound

A method for anesthetizing the skin or the mucous membranes or for treating pruritus in a human or other animal in need of same, said method comprising topically applying to the surface of the skin or mucous membranes of said human or other animal an aqueous composition comprising water, an anesthetically or antipruritically effective amount of at least one compound (1) which modulates the reactivity of nerve fibers, at least one compound (2) which is water-miscible, solubilizes the compound (1), is volatile and is present in sufficient quantity to prevent recrystallization of the compound (1) when the composition is applied to the surface of the skin, and at least one thickener, the weight ratio of water/volatile compounds being greater than or equal to 0.8, the compound (2) being present in a concentration of between 10 and 50% by weight relative to the total weight of the composition, the composition being devoid of any compound, other than water, which does not solubilize the compound (1) and is capable of retarding the evaporation of the volatile compounds present in the composition, and devoid of a compound which solubilizes the compound (1) and is nonvolatile.