  Unitarity of evolution in gravitational collapses implies existence of
macroscopic stable horizonless objects. With such objects in mind, we study the
effects of anisotropy of pressures on the stability of stars. We consider stars
in four or higher dimensions and also stars in M theory made up of
(intersecting) branes. Taking the stars to be static, spherically symmetric and
the equations of state to be linear, we study `singular solutions' and the
asymptotic perturbations around them. Oscillatory perturbations are likely to
imply instability. We find that non oscillatory perturbations, which may imply
stability, are possible if an appropriate amount of anisotropy is present. This
result suggests that it may be possible to have stable horizonless objects in
four or any higher dimensions, and that anisotropic pressures may play a
crucial role in ensuring their stability.
