  In the present work, we study the radial and non-radial perturbative
stability of neutron stars in which the matter is disformally coupled to the
metric. First, we derive the gravitational and the fluid equations of the
neutron star in a static and spherically symmetric background. Then, we
calculate the second-order expansion of the action that describes the dynamics
of both axial and polar modes. From the resulting expressions, we derive the
conditions to avoid gradient and ghost instabilities at the center of the star
and at spatial infinity. In addition, a numerical analysis is performed to
investigate the stability of a particular model with a constant disformal
function denoted as $\Lambda$ in the whole space time. We found that the chosen
model is stable against the gradient instability in a small range of the
constant $\Lambda$.
