In this second paper, we develop a geometrical method to systematically study the singular perturbed problem associated to slowly modulated two-pulse solutions. It enables one to see that the characteristics of these solutions are strongly determined by the flow on a slow manifold and, hence, also to identify the saddle-node bifurcations and bifurcations to classical traveling waves in which the solutions constructed in part I are created and annihilated. Moreover, we determine the geometric

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... gin of the critical maximum wave speeds discovered in part I. In this paper, we also study the central role of the slowly varying inhibitor component of the two-pulse solutions in the pulse-splitting bifurcations. Finally, the validity of the quasi-stationary approximation is established here, and we relate the results of both parts of this work to the literature on self-replication.