Apparatus for drying a moving web includes a first infrared dryer unit having a first infrared treatment gap, a gas-support unit situated substantially immediately after the first infrared dryer unit and having a gas-support unit gap into which web-supporting gas blowings are directed, and a second infrared dryer unit situated after the gas-support unit and having a second infrared treatment gap. The gas-support gap has a width which is less than the width of the first infrared gap and the width of the second infrared treatment gap is less than the width of the first infrared treatment gap and greater than the width of the gas-support gap. In accordance with the method, the web is passed through the first infrared treatment gap so that upon exiting from the gap, its temperature has preferably been raised only to a point where evaporation of water from the web is imminent but has not begun, whereupon the web is passed through the gas-support gap in which web-supporting gas blowings, preferably heated, are directed in regions of both sides of the web, whereupon the web is passed through the second infrared treatment gap where evaporative drying is accomplished.