The new Hamiltonian formulation of complex general relativity first given by Ashtekar (1986) is derived from an action principle for connections in a bundle isomorphic with the complexified tangent bundle. On introducing spinors or orthonormal frames one obtains the theory in the spinorial or triad form respectively, as given by Jacobson and Smolin (1987), and Goldberg (1988). The more usual spinorial or triad Hamiltonian formalisms for real Lorentzian gravity are also recovered. In the present derivation stress is put on geometrical structures involved. Spinors are introduced in two different from standard ways, which causes some structural simplifications to occur in the general complex case. The role of reality conditions is expounded.