  This is the second of a series of papers which give a necessary and
sufficient condition for two essential simple loops on a 2-bridge sphere in a
2-bridge link complement to be homotopic in the link complement. The first
paper of the series treated the case of the 2-bridge torus links. In this
paper, we treat the case of 2-bridge links of slope $n/(2n+1)$ and
$(n+1)/(3n+2)$, where $n \ge 2$ is an arbitrary integer.
