Abstract Double pulse solutions are studied for nerve axon equations including a parameter μ. We assume that there exists a single pulse solution with a non-oscillatory tail. It is known that, when μ is fixed, there exists no double pulse solution. However, when μ varies, a double pulse solution may branch from the single pulse solution. In this paper we obtain a necessary and sufficient condition for the branching of a double pulse solution, and study the direction of the branching.