  A rational number $r$ is called a left orderable slope of a knot $K \subset
S^3$ if the 3-manifold obtained from $S^3$ by $r$-surgery along $K$ has left
orderable fundamental group. In this paper we consider the double twist knots
$C(k,l)$ in the Conway notation. For any positive integers $m$ and $n$, we show
that if $K$ is a double twist knot of the form $C(2m,-2n)$, $C(2m+1, 2n)$ or
$C(2m+1, -2n)$ then there is an explicit unbounded interval $I$ such that any
rational number $r \in I$ is a left orderable slope of $K$.
