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The GNH method is used in this paper to study the Hamiltonian formulation ofthe Euclidean self-dual action. This action can be used to arrive at thecomplex Ashtekar formulation of General Relativity or a real connectionformulation for Euclidean General Relativity. The main result of the paper is aderivation of the Ashtekar formulation for Euclidean gravity without using anygauge fixing. It is interesting to compare this derivation with the onecorresponding to the Holst action. In particular it is worth noting that no``tertiary'' constraints appear in the case considered in the present paper.

Euclidean self-dual gravity: Ashtekar variables without gauge fixing