This thesis aims at providing an example of a cubic Hamiltonian 2 -saddle cycle that after bifurcation can give rise to an alien limit cycle; this is a limit cycle that is not controlled by a zero of the related Abelian integral . To guarantee the existence of an alien limit cycle one can verify generic conditions on the Abelian integral and on the transition map associated to the connections of the 2-saddle cycle . In case ? is a periodic orbit , a non-degenerate elliptic point or a saddle loop , it is well-known that generically the study of the Abelian integral I suf?ces to get full knowledge on the number of limit cycles and their bifurcations . It is known that perturbations from a Hamiltonian 2-saddle cycle can produce limit cycles that are not covered by the Abelian integral , even when it is generic . These limit cycles are called alien limit cycles . This phenomenon cannot appear in the case that is a periodic orbit , a non-degenerate singularity , or a saddle loop . In this thesis , we present a way to study this phenomenon in a particular unfolding of a Hamiltonian 2-saddle cycle , keeping one connection unbroken at the bifurcation. Ihe thesis deals with generic perturbations from a Hamiltonian planar vector ?eld and more precisely with the number and bifurcation pattern of the limit cycles . In this thesis we show that near a 2-saddle cycle , the number of limit cycles produced in unfoldings with one unbroken connection , can exceed the number of zeros of the related Abelian integral , even if the latter represents a stable elementary catastrophe . We however also show that in general , ?nite codimension of the Abelian integral leads to a ?nite upper bound on the local cyclicity . In the treatment , we introduce the notion of simple asymptotic scale deformation.