We discuss the global dynamics of complex Henon maps with a semi-parabolic fixed or periodic point that arise as small perturbations of quadratic polynomials. We then exhibit certain paths in parameter space for which the semi-parabolic structure can be deformed into a hyperbolic structure, and show that the parametric region of semi-parabolic Henon maps with small Jacobian lies in the boundary of a hyperbolic component of the Henon connectedness locus. This is joint work with Raluca Tanase.