PURPOSE: To provide a method and an apparatus for drying and/or cooling a paper web or the like, suitable for the miniaturization and modernization of a paper machine.

CONSTITUTION: When a paper web W is passed over the circumference of a revolving roll 10, etc., on support of the face of a support wire 15 facing the roll 12 and is dried and/or cooled by means of a gas, the gas is blown through openings 44 in the mantle 12 of the roll 10 into a space between the outer face of the roll 10 and the web W supported by the support wire 15, etc., whereby a support zone formed by pressurized gas is formed between the outer face of the roll 10 and the web W. Humidified gas is passed out of the support zone into the interior of the roll 10 through other openings 46 in the mantle 12 of the roll 10 into a system of exhaust ducts placed inside the roll 10.