  We examine the constraints and the reality conditions that have to be imposed
in the canonical theory of 4--d gravity formulated in terms of Ashtekar
variables. We find that the polynomial reality conditions are consistent with
the constraints, and make the theory equivalent to Einstein's, as long as the
inverse metric is not degenerate; when it is degenerate, reality conditions
cannot be consistently imposed in general, and the theory describes complex
general relativity.
