A process for the condensation of sulfur trioxide from hot starting gases comprising the following steps: a) cooling the starting gas to a temperature of 40 to 45O0C in at least one heat exchanger (3) (4), in which a gas is used as cooling medium, b) introducing the cooled starting gas into a condensation device (5), c) condensing the sulfur trioxide in the condensation device (5), in which a liquid chemically inert to sulfur trioxide is used as cooling medium, and d) withdrawing the condensed, liquid sulfur trioxide from the condensation device (5). A plant for carrying out the process comprising: a first and a second heat exchanger (3) (4) comprising supply and discharge conduits for coolant and starting gas, and a condensation device (5), in which a liquid chemically inert to sulfur trioxide is provided as cooling medium.