Abstract: A weaker form of continuity, called Z-continuous functions is introduced by Singal and Nimse [17 ] in 1997. A function is called Z-continuous if the inverse image of a cozero set in Y is open in X. In the section 3 of this paper, a weaker form of this function , called Z-precontinuous function is introduced and their properties are studied and in section 4, a stronger of this function, called pre Z-continuous functions, is introduced and their properties are studied .