  We study the oscillations of neutron and strange stars in $R^2$ gravity. More
precisely the nonradial $f$-modes are examined and the differences with pure
general relativity are investigated. Using these results we build several
gravitational wave asteroseismology relations. Our goal is to determine up to
what extend these relations are equation of state independent and whether they
deviate enough from general relativity in order to produce an observable
effect. The results show that the differences coming from $R^2$ gravity are up
to 10\% and that will be difficult to be observed in the near future. On the
other hand the small deviations in some of the asteroseismology relations show
that they are not only equation of state independent, but they are also quite
insensitive to the gravitational theory. That is why solving the inverse
problem can give us quite robust estimates of the neutron star parameters.
