In this paper, we introduce the L-separation axioms GT21 2 and GT5 using the notion of L- neighborhood filter defined by G¨ahler in 1995. We define also the axiom GT6 depending on the notion of L-numbers presented by G¨ahler in 1994. Denote by GTi-space for the L-topological space which is GTi, i = 21 2 , 5, 6. The GTi-spaces, i = 0, 1, 2, 3, 31 2 , 4 had been introduced and studied by the author in 2001 - 2004 in separate six papers. All the axioms GTi are based only on usual points and ordinary sets and they are the usual ones in the classical case L = {0, 1}. It is shown that the axioms GTi, i = 21 2 , 5, 6 fulfill many properties analogous to the usual axioms and moreover, the initial and the final of GTi-spaces are also GTi-spaces, i = 21 2 , 5, 6. Keywords: L-neighborhood filters; L-real numbers; GTi-spaces; GT21 2 -spaces; Completely normal spaces; GT5-spaces; Perfectly normal spaces; GT6-spaces.