A panel fastening system, especially for floor panels. The floor panels are fitted with retaining profiles on their edges, whereby the retaining profile of a front edge and the retaining profile of the opposite back edge and the retaining profile of a left edge and the retaining profile of the opposite right edge of a panel match each other in such a way that similar panels can be fixed to one another. The mutually matching retaining profiles have complementary hook elements that can be hooked into one another and the hook elements have retaining surfaces by means of which the panels are held against each other when mounted in such a way that a gap-free surface is obtained.