  We prove the existence of global weak solutions with finite energy to some
two-fluid systems with magnetic field and the results suit for corresponding
two-fluid systems. The proof method is mainly inspired by Novotn\'y et al. and
Vasseur et al. For $academic~magnetic$ $ bi\text{-}fluid~ system$, we focus on
the case of pressure law with ideal gases and the new ingredient is that we can
make the proof more explicit without using the preposed hypotheses and remove
some unnecessary conditions of the main theorem in Novotn\'y et al. Meanwhile,
the same proof method can be used to $real~magnetic$ $ bi\text{-}fluid~ system$
combined with pressure law proposed in Vasseur et al.
