  We study the influence of the isovector-scalar meson on the spinodal
instabilities and the distillation effect in asymmetric non-homogenous nuclear
matter under strong magnetic fields, of the order of $10^{18}-10^{19}$ G.
Relativistic nuclear models both with constant couplings (NLW) and with density
dependent parameters (DDRH) are considered. A strong magnetic field can have
large effects on the instability regions giving rise to bands of instability
and wider unstable regions. It is shown that for neutron rich matter the
inclusion of the $\delta$ meson increases the size of the instability region
for NLW models and decreases it for the DDRH models. The effect of the $\delta$
meson on the transition density to homogeneous $\beta$-equilibrium matter is
discussed. The DDRH$\delta$ model predicts the smallest transition pressures,
about half the values obtained for NL$\delta$.
