In this paper, the notion of Sß-compactness is introduced in Ltopological spaces by means of open ßà-cover. It is a generalization of Lowen s strong compactness, but it is different from Wang s strong compactness. Ultra-compactness implies Sß-compactness. Sß-compactness implies fuzzy compactness. But in general N-compactness and Wang s strong compactness need not imply Sß-compactness