A new form of ß-compactness is introduced in L-topological spaces by means of ß-open L-sets and their inequality where L is a complete de Morgan algebra. This new form doesn t rely on the structure of basis lattice L. It can also be characterized by means of ß-closed L-sets and their inequality. When L is a completely distributive de Morgan algebra, its many characterizations are presented. Meanwhile countable ß-compactness and the ß-Lindelöf property are also researched