  This paper is concerned with the structural stability of spherical horizons.
By this we mean stability with respect to variations of the second member of
the corresponding differential equations, corresponding to the inclusion of the
contribution of operators quadratic in curvature. This we do both in the usual
second order approach (in which the independent variable is the spacetime
metric) and in the first order one (where the independent variables are the
spacetime metric and the connection field). In second order, it is claimed that
the generic solution in the asymptotic regime (large radius) can be matched not
only with the usual solutions with horizons (like Schwarzschild-de Sitter) but
also with a more generic (in the sense that it depends on more arbitrary
parameters) horizonless family of solutions. It is however remarkable that
these horizonless solutions are absent in the {\em restricted} (that is, when
the background connection is the metric one) first order approach.
