  We discuss reality conditions and the relation between spacetime
diffeomorphisms and gauge transformations in Ashtekar's complex formulation of
general relativity. We produce a general theoretical framework for the
stabilization algorithm for the reality conditions, which is different from
Dirac's method of stabilization of constraints. We solve the problem of the
projectability of the diffeomorphism transformations from
configuration-velocity space to phase space, linking them to the reality
conditions. We construct the complete set of canonical generators of the gauge
group in the phase space which includes all the gauge variables. This result
proves that the canonical formalism has all the gauge structure of the
Lagrangian theory, including the time diffeomorphisms.
