A process and apparatus for continuous welding by a laser beam of guided and abutted strips or plates which lie in a plane comprises supplying a follow-up process gas to a welding location and thereafter, cooling the welding location by applying a sprayed-on coolant to an area adjacent to the welding location. The coolant comprises a mixture of water and gas, and is sprayed onto the strips or plates in the form of a flat jet. The flat jet extends towards the welding location and lies in a plane perpendicular to the plane of the strips or plates. The leading edge of the flat jet forms an acute angle with the laser beam.