  We show in this paper that it is possible to formulate General Relativity in
a phase space coordinatized by two $SO(3)$ connections. We analyze first the
Husain-Kucha\v{r} model and find a two connection description for it.
Introducing a suitable scalar constraint in this phase space we get a
Hamiltonian formulation of gravity that is close to the Ashtekar one, from
which it is derived, but has some interesting features of its own. Among them a
possible mechanism for dealing with the degenerate metrics and a neat way of
writing the constraints of General Relativity.
