Spatial and dynamical effects in double phase conjugate mirrors are in
vestigated analytically and numerically. A variety of spatial and temp
oral effects are observed, such as beam-bending, self-defocusing, mode
oscillations and irregular pattern formation. We conclude that in mor
e than one spatial dimension the double phase conjugate mirror is a co
nvective oscillator. For strong beam couplings and strong diffraction
we find that the oscillation threshold is not well defined, and that t
he double phase conjugate mirror becomes unstable. An improved agreeme
nt with experimental results is obtained.