  We analyse the mathematical underpinnings of a mixed hyperbolic-elliptic form
of the Einstein equations of motion in which the lapse function is determined
by specified mean curvature and the shift is arbitrary. We also examine a new
recently-published first order symmetric hyperbolic form of the equations of
motion. This paper is dedicated to Andre Lichnerowicz on the occasion of his
80th birthday and will appear in a volume edited by G. Ferrarese.
