The authors derive a differential equation for a self-parallel curve deviation on a statistical manifold [for the latter see S.-I. Amari, Differential-geometrical methods in statistics. (1985; Zbl 0559.62001)]. It is assumed that the self-parallel curves are neighbouring both in position and velocity, and also with respect to a one-parameter family of linear connections. The cases of the Gaussian manifold and the manifold of multinomial distributions are considered in detail.