%0 Journal Article %T Homotopically equivalent simple loops on 2-bridge spheres in 2-bridge link complements (II) %A Donghi Lee %A Makoto Sakuma %J Mathematics %D 2011 %I arXiv %X 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. %U http://arxiv.org/abs/1103.0856v4