  Spatially localized and periodic field patterns in periodically modulated
optical parametric amplifiers and oscillators are studied. In the degenerate
case (equal signal and idler beams) we elaborate the systematic method of
construction of the stationary localized modes in the amplifiers, study their
properties and stability. We describe a method of constructing periodic
solutions in optical parametric oscillators, by adjusting the form of the
external driven field to the given form of either signal or pump beams.
