  We study the dynamics of Einstein's equations in Ashtekar's variables from
the point of view of the theory of hyperbolic systems of evolution equations.
We extend previous results and show that by a suitable modification of the
Hamiltonian vector flow outside the sub-manifold of real and constrained
solutions, a symmetric hyperbolic system is obtained for any fixed choice of
lapse-shift pair, without assuming the solution to be a priori real. We notice
that the evolution system is block diagonal in the pair $(\sigma^a,A_b)$, and
provide explicit and very simple formulae for the eigenvector-eigenvalue pairs
in terms of an orthonormal tetrad with one of its components pointing along the
propagation direction. We also analyze the constraint equations and find that
when viewed as functions of the extended phase space they form a symmetric
hyperbolic system on their own. We also provide simple formulae for its
eigenvectors-eigenvalues pairs.
