BIFURCATION AT COMPLEX INSTABILITY Merce Olle(1) and Daniel Pfenniger(2) (1) Dept. Matematica Aplicada I, ETSEIB Diagonal 647, 08028 Barcelona (Spain) (2) Observatoire de Geneve, CH-1290 Sauverny (Switzerland) E-mail> Olle@ma1.upc.es Daniel.Pfenniger@obs.unige.ch Abstract. The properties of motion close to the transition of a stable family of periodic orbits to complex instability is investigated with two symplectic 4D mappings, natural extensions of the standard mapping. As for other types of instabilities new families of periodic orbits may bifurcate at the transition, but, more generally, families of isolated invariant curves bifurcate, similar to but distinct from a Hopf bifurcation. The evolution of the stable invariant curves and their bifurcations are described.