  The equations of state for degenerate electron and neutron gases are studied
in the presence of magnetic fields. After including quantum effects to study
the structural properties of these systems, it is found that some
hypermagnetized stars can be unstable based on the criterium of stability of
pressures. Highly magnetized white dwarfs should collapse producing a supernova
type Ia, whilst superstrongly magnetized neutron stars cannot stand their own
magnetic field and must implode, too. A comparison of our results with a set of
the available observational data of some compact stars is also presented, and
the agreement between this theory and observations is verified.
