  In this work, we present results on stability and hyperbolicity of equilibria
for a scalar nonlocal one-dimensional quasilinear parabolic problem. We show
that this nonlocal version of the well-known Chafee-Infante equation bares some
resemblance with the local version. However, its nonlocal characteristc
requires a fine analysis of the spectrum of the associated linear operators, a
lot more ellaborated than the local case. The saddle point property of
equilibria is shown to hold for this quasilinear model.
