A process for the metathesis of olefins, comprising bringing said olefins into contact with a catalyst which has been activated by heating to a temperature in the range 100° C. to 1000° C. in an atmosphere of non-reducing gas, said catalyst comprising at least one inorganic material constituted by at least two elementary spherical particles, each of said elementary spherical particles comprising metal oxide particles with a size of at most 300 nm and containing at least one metal selected from tungsten, molybdenum, rhenium, cobalt, tin, ruthenium, iron and titanium, used alone or as a mixture, said metal oxide particles being present within a mesostructured matrix based on an oxide of at least one element Y selected from silicon, aluminium, titanium, tungsten, zirconium, gallium, germanium, tin, antimony, lead, vanadium, iron, manganese, hafnium, niobium, tantalum, yttrium, cerium, gadolinium, europium and neodymium and a mixture of at least two of these elements, said mesostructured matrix having a pore size in the range 1.5 to 50 nm and having amorphous walls with a thickness in the range 1 to 30 nm and said elementary spherical particles having a maximum diameter of 200 μm.