Abstract: The invention relates, in particular, to supported transition metal complexes based on a polystyrene matrix comprising structural units of the formula (Ia): or supported transition metal complexes based on a silica gel matrix comprising structural units of the formula (II): where the radicals and indices have the meanings given in the description. The invention also relates to the use of the supported transition metal complexes in catalysis and corresponding processes for the transition metal-catalyzed conversion of starting material(s) into product(s). In particular, the invention relates to the field of olefin metathesis.