A fastening system for floor panels, which has profiles on small faces of the panels. Opposite retaining profiles match so that similar panels can be interlinked. The panels have opposite first retaining profiles configured so on a panel in first line, a new panel can be locked in second line by attaching the new panel to the installed panel at an angle relative to the installed panel and then swiveling it down into the plane of the installed panel. The panel has opposite second retaining elements that have corresponding hook elements. A hook connection can be established by a hook element of the new panel and hook element of a panel already installed in second line by swiveling the new panel. Every hook connection is associated with an additional locking element that prevents the release of the hook connection in a direction perpendicular to the plane of the installed panels.