An assembly of support buoys for a flexible submarine pipeline which is designed for the transport of hydrocarbons. A plurality of buoys which can be installed gradually on at least one portion of the flexible submarine pipeline. A fixing device blocks translational movement of the buoys on the portion of the pipeline. The fixing device includes a hitching or coupling line which connects each of the buoys successively to one another. The translational movement of each of the buoys is gradually blocked on the coupling line. Connecting devices maintain the coupling line taut at locations along the portion of the pipeline.