By the process of the present invention the activity of heterogeneous catalysts for reactions at normal and low pressures is restored or maintained. These catalysts can lose their activity as a result of the deposition, physisorption or chemisorption of organic or inorganic deactivating substances which are carried over into the reaction system or are formed as the result of side reactions in a chemical synthesis carried out with the aid of the catalyst. The activity is restored or maintained by using a pressure greater than the critical pressure of the fluid phase and a temperature higher than or equal to the critical temperature of the fluid phase. In this process, the pressure and temperature are applied for a period such that the deactivating substances are either removed from the catalyst or are not initially deposited thereon or absorbed or formed.