  The Einstein evolution equations have been written in a number of symmetric
hyperbolic forms when the gauge fields--the densitized lapse and the shift--are
taken to be fixed functions of the coordinates. Extended systems of evolution
equations are constructed here by adding the gauge degrees of freedom to the
set of dynamical fields, thus forming symmetric hyperbolic systems for the
combined evolution of the gravitational and the gauge fields. The associated
characteristic speeds can be made causal (i.e. less than or equal to the speed
of light) by adjusting 14 free parameters in these new systems. And 21
additional free parameters are available, for example to optimize the stability
of numerical evolutions. The gauge evolution equations in these systems are
generalizations of the ``K-driver'' and ``Gamma-driver'' conditions that have
been used with some success in numerical black hole evolutions.
