Abstract: A laser welding process includes the steps of deflecting, with an oscillating frequency of at least 100 Hz, a collimated and focused laser measuring beam, intensity-modulated with a frequency of at least 200 kHz, across the path of the weld groove during co-travel with the laser welding beam along the weld groove; directing the laser measuring beam to the workpieces; causing the laser measuring beam to impinge on the workpieces at a distance of maximum 10 mm from the central longitudinal axis of the laser welding beam; sensing, by an electro-optical sensor having a single light-sensitive element, rays of the laser measuring beam reflected by the workpieces; generating, by the sensor, measuring signals in response to the sensed reflected rays; applying follow-up signals in response to the measuring signals, and correcting the position of the laser welding beam by the follow-up device in response to the follow-up signals applied thereto.