Guo-Feng Wen - School of Management Science and Engineering, Shandong Institute of Business and Technology, Yantai ۲۶۴۰۰۵, P. R. China
Fu-Gui Shi - Department of Mathematics, Beijing Institute of Technology, Beijing,۱۰۰۰۸۱, P. R. China
Hong-Yan Li - School of Mathematics and Information Science, Shandong Institute of Business and Technology, Yantai ۲۶۴۰۰۵, P. R. China

In this paper, the notion of almost S^{*}-compactness in L-topologicalspaces is introduced following Shi’s definition of S^{*}-compactness. The propertiesof this notion are studied and the relationship between it and otherdefinitions of almost compactness are discussed. Several characterizations ofalmost S^{*}-compactness are also presented.

L-topology, beta_{a}-cover, Q_{a} -cover, S^{*}-compactness, Almost S^{*}-compactness