A process for the removal of gaseous, liquid and solid heavy metals or their compounds, from fumes deriving from combustion processes or from the production synthetic gas, wherein the fumes are washed with an aqueous phase, wherein the process comprises the following steps: b) flue gas washing with an aqueous phase having a pH between 0.7 and 3.3, and comprising one or more oxidizing agents and one or more acid compounds, said oxidizing agents being inorganic oxidizing compounds having an oxidation potential, at a pH comprised between 0.7 and 3.3, higher than 1.5 eV, wherein the heavy metals or their compounds, soluble in said aqueous phase, are converted into anion compounds and simultaneously the particles of heavy metals or their compounds which are insoluble in said aqueous phase are wetted, to allow the transfer of them into said aqueous phase; c) cooling and partial condensation of water vapour contained in the flue gas, separation of a condensed aqueous phase, optionally recycling the condensed phase to the combustion chamber (combustor); d) discharge into the environment of flue gas substantially free from heavy metals or their compounds, carried out with the following steps: e°) optionally, separation of the insoluble particulate of heavy metals, or their compounds, from the aqueous phase obtained in step b); e) treatment of the aqueous phase obtained in b) or in optional step e°) with anionic exchange resins to remove the heavy metals or their compounds soluble in the aqueous phase; e') optionally, separation of the insoluble particulate of heavy metals, or their compounds, from the aqueous phase obtained in step e); f) optionally, discharge of the aqueous phase obtained in e') substantially free from heavy metals or their compounds into the environment. g) optionally, recovery by regeneration of the anionic exchange resins with an aqueous solution. b) flue gas washing with an aqueous phase having a pH between 0.7 and 3.3, and comprising one or more oxidizing agents and one or more acid compounds, said oxidizing agents being inorganic oxidizing compounds having an oxidation potential, at a pH comprised between 0.7 and 3.3, higher than 1.5 eV, wherein the heavy metals or their compounds, soluble in said aqueous phase, are converted into anion compounds and simultaneously the particles of heavy metals or their compounds which are insoluble in said aqueous phase are wetted, to allow the transfer of them into said aqueous phase; c) cooling and partial condensation of water vapour contained in the flue gas, separation of a condensed aqueous phase, optionally recycling the condensed phase to the combustion chamber (combustor); d) discharge into the environment of flue gas substantially free from heavy metals or their compounds, carried out with the following steps: e°) optionally, separation of the insoluble particulate of heavy metals, or their compounds, from the aqueous phase obtained in step b); e) treatment of the aqueous phase obtained in b) or in optional step e°) with anionic exchange resins to remove the heavy metals or their compounds soluble in the aqueous phase; e') optionally, separation of the insoluble particulate of heavy metals, or their compounds, from the aqueous phase obtained in step e); f) optionally, discharge of the aqueous phase obtained in e') substantially free from heavy metals or their compounds into the environment. g) optionally, recovery by regeneration of the anionic exchange resins with an aqueous solution. d) discharge into the environment of flue gas substantially free from heavy metals or their compounds, carried out with the following steps: e°) optionally, separation of the insoluble particulate of heavy metals, or their compounds, from the aqueous phase obtained in step b); e) treatment of the aqueous phase obtained in b) or in optional step e°) with anionic exchange resins to remove the heavy metals or their compounds soluble in the aqueous phase; e') optionally, separation of the insoluble particulate of heavy metals, or their compounds, from the aqueous phase obtained in step e); f) optionally, discharge of the aqueous phase obtained in e') substantially free from heavy metals or their compounds into the environment. g) optionally, recovery by regeneration of the anionic exchange resins with an aqueous solution.