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We continue to investigate the dynamics of collisionless systems of particlesinteracting via additive $r^{-\alpha}$ interparticle forces. Here we focus onthe dependence of the radial-orbit instability on the force exponent $\alpha$.By means of direct $N$-body simulations we study the stability of equilibriumradially anisotropic Osipkov-Merritt spherical models with Hernquist densityprofile and with $1\leq\alpha<3$. We determine, as a function of $\alpha$, theminimum value for stability of the anisotropy radius $r_{as}$ and of themaximum value of the associated stability indicator $\xi_s$. We find that, fordecreasing $\alpha$, $r_{as}$ decreases and $\xi_s$ increases, i.e.longer-range forces are more robust against radial-orbit instability. Theisotropic systems are found to be stable for all the explored values of$\alpha$. The end products of unstable systems are all markedly triaxial withminor-to-major axial ratio $>0.3$, so they are never flatter than an E7 system.

Radially anisotropic systems with $r^{-\alpha}$ forces. II: radial-orbit instability