Abstract: During laying of a pipeline on a surface located under water, on a vessel a pipe is fitted to a pipe string of the pipeline, in each case during a fitting step. Herein during the fitting step the vessel is moved substantially continuously in lengthwise direction of the pipe string while a pipe is fitted to the pipe string by means of positioning means moved relative to the vessel and by means of welding means moved relative to the vessel. According to the invention, a train of positioning means, welding means and clamping means is moved during an operational phase relative to the vessel in lengthwise direction of the pipe string in principle together with the pipe string and during a resetting phase set between two successive operational phases this train is displaced in the direction of the prow of the vessel relative to the pipe string and relative to the vessel.