  A two-dimensional model of an electron moving under the influence of an
attractive zero-range potential as well as external magnetic and electric
fields is analyzed. We prove by numerical investigations that there are formed
such resonances which manifest a peculiar dependance on the electric field
intensity, i.e., although the electric field increases, the lifetime of these
resonance states grows up. It is explained that this phenomenon, called further
\textit{the stabilization}, is a close consequence of
\textit{quantum-mechanical vortices} induced by the magnetic field and
controlled by the electric field strength. In order to get more information
about these vortices the phase of wavefunctions as well as the probability
current for these stable resonances are investigated.
