The invention relates to a fastening system (1) for rectangular, tabular panels (2, 3, 10), especially floor panels. Comprising retaining profiles disposed on the small faces of said panels (2, 3, 10). Opposite retaining profiles match said retaining profiles in such a manner that similar panels (2, 3, 10) can be interlinked. The panels are provided with opposite first retaining profiles that are configured in such a manner that on a panel (2, 3, 10) being in first line a new panel (2) can be locked in second line by attaching the new panel (2) to the installed panel (3) at a temporary angle relative to the installed panel (3) and then swiveling it down into the plane of the installed panel (3). The panel further comprises opposite second retaining elements that comprise corresponding hook elements (6, 7). A hook connection (8) can be established by means of one of the hook elements (6, 7) of the new panel (2) and a hook element (6, 7) of a panel (3) that is already installed in second line by swiveling down the new panel (2). Every hook connection (8) is associated with an additional locking element (13, 22, 26, 27, 34, 35, 36, 40, 46) that prevents, in the hooked state of two panels (2, 3, 10), the hook connection (8) from being released in a direction perpendicular to the plane of the installed panels (2, 3 10).