We present a formal theory and detailed calculations for phase-depende
nt laser-atom interactions involving autoionizing states. First, throu
gh simple models, we demonstrate that the simultaneous one-and three-p
hoton excitation of one or two neighboring autoionizing states can exh
ibit profound changes of the line shape, as the relative phase of the
two fields is varied from 0 to pi. Through a proper choice of the fiel
d intensities and the phase, we obtain analytical results showing that
one can cancel the transition to the discrete or the continuum part o
f the wave function, thereby leading to a flat or a completely symmetr
ic line shape, respectively. At higher intensities, additional effects
come into play, providing additional coupling between the discrete an
d continuum parts, which also exhibits a phase dependence. Finally, ou
r theory is applied to a much more complex situation in Xe, involving
many channels, not amenable to simple analytical expressions, but exhi
biting nevertheless equally profound effects, including a modification
of the branching ratio of two different products. The theory, which i
s here developed for atomic autoionization, is in fact fairly general
and should pertain to related problems in any system involving discret
e states embedded in continua.