  In Cao, Du, Li and Li [8], a nonlocal diffusion model with free boundaries
extending the local diffusion model of Du and Lin [12] was introduced and
studied. For Fisher-KPP type nonlinearities, its long-time dynamical behaviour
is shown to follow a spreading-vanishing dichotomy. However, when spreading
happens, the question of spreading speed was left open in [8]. In this paper we
obtain a rather complete answer to this question. We find a condition on the
kernel function such that spreading grows linearly in time exactly when this
condition holds, which is achieved by completely solving the associated
semi-wave problem that determines this linear speed; when the kernel function
violates this condition, we show that accelerating spreading happens.
