A folding, or interfolding, machine comprising: - a folding, or interfolding, section, arranged to fold, or interfold, a web of paper or a plurality of sheets of paper into a plurality of panels, according to a predetermined folding, or interfolding, configuration; said machine characterised in that said folding, or interfolding, section, comprises: - a first and a second support (41a,41b) facing each other in a central zone and having respective lateral surfaces (42a,42b) provided with at least one peripheral suction groove (43a,43b) extending on said lateral surface (42a,42b) for a predetermined length, said, or each, peripheral suction groove (43a,43b) pneumatically connected to an air suction system in such a way to define a corresponding suction portion (44a,44b) on the lateral surface (42a,42b) of the respective support (41a,41b); - a first and a second suction belt (45a,45b) arranged to move respectively along a first and a second closed trajectory (46a,46b), said first and second closed trajectory comprising, respectively, said suction portions (44a,44b) of said first and second support (41a,41b), said first and second suction belt (45a,45b) configured to air-tightly engage with said suction portions and providing at least one through hole (47a,47b) arranged to be positioned at a respective suction portion (44a,44b) for causing a suction on said web, or said sheets; - a driving device configured to move said first and second suction belt (45a,45b) with respect to said support (41a,41b), in such a way that said through holes (47a,47b) of the first, or the second, belt (45a,45b) are located at said central zone shifted from each other. - a folding, or interfolding, section, arranged to fold, or interfold, a web of paper or a plurality of sheets of paper into a plurality of panels, according to a predetermined folding, or interfolding, configuration; - a first and a second support (41a,41b) facing each other in a central zone and having respective lateral surfaces (42a,42b) provided with at least one peripheral suction groove (43a,43b) extending on said lateral surface (42a,42b) for a predetermined length, said, or each, peripheral suction groove (43a,43b) pneumatically connected to an air suction system in such a way to define a corresponding suction portion (44a,44b) on the lateral surface (42a,42b) of the respective support (41a,41b); - a first and a second suction belt (45a,45b) arranged to move respectively along a first and a second closed trajectory (46a,46b), said first and second closed trajectory comprising, respectively, said suction portions (44a,44b) of said first and second support (41a,41b), said first and second suction belt (45a,45b) configured to air-tightly engage with said suction portions and providing at least one through hole (47a,47b) arranged to be positioned at a respective suction portion (44a,44b) for causing a suction on said web, or said sheets; - a driving device configured to move said first and second suction belt (45a,45b) with respect to said support (41a,41b), in such a way that said through holes (47a,47b) of the first, or the second, belt (45a,45b) are located at said central zone shifted from each other.