  In the present paper we study models of neutron stars in a class of extended
scalar-tensor Gauss-Bonnet (ESTGB) theories for which the scalar degree of
freedom is exited only in the strong curvature regime. We show that in the
framework of the ESTGB theories under consideration there exist new neutron
star solutions which are formed via spontaneous scalarization of the general
relativistic neutron stars. In contrast to the spontaneous scalarization in the
standard scalar-tensor theories which is induced by the presence of matter, in
our case the scalarization is induced by the spacetime curvature.
