Abstract: A method for in vitro selection, from a library of catalyst molecules, of a catalyst molecule of interest having a relatively more efficient specific catalytic activity of interest, as compared to the rest of the catalyst molecules within said library, and wherein said in vitro selection method is characterized by that it allows multiple catalytic activity turn-overs (i.e. substrate to product catalytic activity turn-overs), by the catalyst molecule of interest, before it is finally collected. The method is based on using one or more reagent(s) which are capable of converting a product generated by a catalyst molecule of interest back into the substrate for said catalyst of interest.