  We study the stability of travelling wave solutions to dispersion generalized
Benjamin--Ono type equations with the double power nonlinearities $|u|^{p-1}u +
|u|^{q-1}u \ (1 < p < q < \infty)$. We prove that travelling wave solutions
constructed by ground states are stable if $p$ is $L^{2}$-subcritical and
speeds of waves are sufficiently small by showing the coercivity of the
linearized operator around ground states, which is introduced by
Grillakis-Shatah-Strauss (1987).
