  We study the stability of static spherically symmetric exact solutions of
Einstein equations coupled with nonlinear electrodynamics, in the magnetic
sector. These solutions satisfy the heuristic model proposed by
Ashtekar-Corichi-Sudarsky for hairy black holes, meaning that the horizon mass
is related to their Arnowitt-Deser-Misner (ADM) mass and to the corresponding
particle-like solution. We test the unstability conjecture that emerges for
hairy black holes and it turned out that it becomes confirmed except for the
Einstein-Born-Infeld solutions.
