  We discuss neutron stars with strong magnetic mean fields in the framework of
Extended Theories of Gravity. In particular, we take into account models
derived from $f(R)$ and $f(\cal G)$ extensions of General Relativity where
functions of the Ricci curvature invariant $R$ and the Gauss-Bonnet invariant
${\cal G}$ are respectively considered. Dense matter in magnetic mean field,
generated by magnetic properties of particles, is described by assuming a model
with three meson fields and baryons octet. As result, the considerable
increasing of maximal mass of neutron stars can be achieved by cubic
corrections in $f(R)$ gravity. In principle, massive stars with $M> 4
M_{\odot}$ can be obtained. On the other hand, stable stars with high
strangeness fraction (with central densities $\rho_{c}\sim 1.5-2.0$
GeV/fm$^{3}$) are possible considering quadratic corrections of $f(\cal {G})$
gravity. The magnetic field strength in the star center is of order $6-8\times
10^{18}$ G. In general, we can say that other branches of massive neutron stars
are possible considering the extra pressure contributions coming from gravity
extensions. Such a feature can constitute both a probe for alternative theories
and a way out to address anomalous self-gravitating compact systems.
