The methods of controlling a catalyst's selectivity by holding its surface (and in special cases its sub-surface) layer in non-stationary states towards the reagents are discussed. This may be achieved by the use of (a) a membrane catalyst; (b) a fluid bed; (c) a riser reactor; (d) periodical changes of the process parameters or catalyst circulation between the reactor and the regenerator; (e) a chromatographic regime; (f) a self-oscillating or stochastic regime. The membrane catalyst produces a non-stationary state of the catalyst surface more easily than do the other methods and for a longer period of time. This propensity of the membrane catalyst is especially important for small-scale industrial installations and for producing ultrapure substances. The transfer of one reagent through the catalyst, for example through a palladium-based septum, increases the selectivity of the hydrogenation of triple bonds into double bonds and of, say, one double bond in a cyclic diene in comparison with normal hydrogenation by the same catalyst. Selectivity of the hydrogenation is a function of hydrogen content in the membrane catalyst. It is shown that hydrogen atoms extracted from the sub-surface layer of the membrane catalyst participate in the hydrogenation process.