The equations of state for degenerate electron and neutron gases are studied in the presence of magnetic fields. After including quantum effects in the investigation of the structural properties of these systems, it is found that some hypermagnetized stars can be unstable according to the criterion of stability of pressures. Highly magnetized white dwarfs should collapse producing a supernova type Ia, while superstrong 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.