In this paper, the concepts of L-fuzzy countable compactness and the L-fuzzy Lindelöf property are introduced in L-fuzzy topological spaces, where L is a completely distributive DeMorgan algebra. An L-fuzzy compact L-fuzzy set is L-fuzzy countably compact and has the L-fuzzy Lindelöf property. An L-fuzzy set having the L-fuzzy Lindelöf property is L-fuzzy countably compact if and only if it is L-fuzzy compact. Many characterizations of L-fuzzy countable compactness and the L-fuzzy Lindelöf property are presented.