In this paper, we have shown that a commutative l-group resembles like a commutative l-group, and most of the features of l-groups are retained by the l-loop. After developing some of the relevant properties of an l-loop, we have characterised its positive cone, obtained a necessary and sufficient condition for an l-loop to become an l-group and for it to be totally ordered.

Keywords: Loops, partial order, lattices, ordered abelian groups.