A composition for topical application to a part of the body comprises a local anaesthetic and optionally a vasodilator as active ingredient dissolved in a blend of volatile and non-volatile solvents of different solvating capacities for the active ingredient. The vasodilator may comprise glyceryl trinitrate and the local anaesthetic may comprises an anaesthetic of the aminoamide or aminoester type. The volatile solvent may comprise a mixture of water with a C.sub.1-C.sub.5 alcohol and the non-volatile solvent may comprise a polyhydric alcohol and optionally a glycol. A low-concentration vasodilator-containing composition is also described. The compositions allow a "virtual injection" of the active ingredient to be delivered transdermally without general systemic uptake.