Abstract: An understructure for a panel lining, such as a panel false ceiling, and for securing the lining panels to the building surface to be lined, including a first set of parallel elongate rails and a second set of parallel elongate rails extending transversely thereto, the two sets of rails being of same or similar cross-section and the rails of the first set overlying the rails of the second set at cross-over points, cross-over connections being provided to secure the rails of the first set to the rails of the second set. These connections include an upper connecting part engagable over the rail of the first set and a lower clamping part engagable over the rail of the second set at the associated cross-over point to hold the cross-over connection to the rail of the second set.