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