WE EXTEND THE CONCEPT OF STRONGLY Compact AND SEMI Compact SPACES. A SPACE (X, T) IS SAID TO BE SEMI L-Compact (RESP. STRONGLY L-Compact) IF EVERY COVER OF X BY SEMI-OPEN (RESP.PREOPEN) SETS HAS A SUBCOVER OF X WHOSE CARDINALITY IS LESS THAN L, WHERE L IS THE LEAST INFINITE CARDINAL NUMBER WITH THIS PROPERTY. WE CHARACTERIZE SEMI L-Compact AND STRONGLY L-Compact SPACES.