Composite materials having high cohesive strength, formed from at least one polymer and from at least one compound selected from among mineral oxides, aluminosilicates and active carbon, are characterized by a mean particle size of at least 100 mm, a pore volume (Vd1) formed by pores having a diameter ranging from 3.6 to 1,000 nm, equal to at least 0.2 cm3/g, a cohesive strength such that its content of particles having a size of less than 100 mm, obtained after being subjected to an air pressure of 2 bar, of less than 1.5%, preferably 0.0%, by volume; such composite materials are formed into useful liquid supports, catalyst supports, additives, or liquid or gas filters, in particular into cigarette filters.