Method for solubilising asphaltenes in an asphaltenes-containing hydrocarbon mixture by adding thereto an effective amount of a dendrimeric compound, and a hydrocarbon mixture comprising, in addition to hydrocarbons, asphaltenes and at least one dendrimeric compound. Preferably, the dendrimeric compound is a hyperbranched polyester amide, more preferably a polyester amide built up from succinic anhydride, diisopropanolamine, functionalised with poly (isobutenyl) succinic anhydride.