The coupling of two autoionizing states or of a discrete and an autoionizin
g state by a strong laser field is studied analytically as well as numerica
lly. The motion of the complex energies is traced as a function of the fiel
d strength for different field frequencies and atomic parameters. Most inte
resting is the critical region where a crossing (or an avoided crossing) of
the trajectories occurs. At this critical field intensity, level repulsion
in the complex plane occurs. With further increasing intensity, the comple
x energies move differently. When the resonances are coupled mainly via one
common continuum, resonance trapping dominates, i.e. a short- and a long-l
ived resonance state are formed (level repulsion along the imaginary axis).
When, however, the direct coupling dominates, level repulsion along the re
al axis takes place. Population trapping (defined by a vanishing decay widt
h of one of the states at finite intensity) results from the interplay of t
he direct coupling of the states and their coupling via the continuum. We a
lso studied the corresponding variation of the cross section for ionization
of a laser-driven atom by the probe field.