Abstract: By a process of cleaning flue gases, both solid particles and nitrogen oxides and sulphur dioxide are removed from the flue gas prior to the discharging into the atmospheric air. In order to ensure that almost all the content of sulphur dioxide and nitrogen oxides is removed from the flue gas, said flue gas is initially carried through a shower of aqueous liquid and subsequently through a heat exchanger, in which its temperature is lowered to about 20.degree.-30.degree. C., and then through a film of alkaline liquid, and finally through a second shower of aqueous liquid to pass a sulphuric acid neutralizing liquid in a container before the discharging into the atmospheric air. As a result a simultaneous possibility of utilizing the heat of the flue gas is ensured by means of the heat exchanger. A cleaning plant for carrying out the process comprises an apparatus (2), through which the flue gas cleaned of solid particles is carried.