A contact system for production of sulphuric acid of a high yield, especially of pyrite or roaster gases by means of the contact method in a system of single- or double-stage conversion consists of a number of separate contact units, each of them including one layer of a catalyst and a heat exchanger. A layer of a catalyst is in the form of a vertical cylinder, and in the space enclosed by the said layer a heat exchanger is situated. A contact apparatus is provided with a helical guide of the gas supplied onto a layer of the catalyst.