  We discuss an equivalence between the Baumgarte-Shapiro-Shibata-Nakamura
(BSSN) formulation of the Einstein evolution equations, a subfamiliy of the
Kidder--Scheel--Teukolsky formulation, and other strongly or symmetric
hyperbolic first order systems with fixed shift and densitized lapse. This
allows us to show under which conditions the BSSN system is, in a sense to be
discussed, hyperbolic. This desirable property may account in part for the
empirically observed better behavior of the BSSN formulation in numerical
evolutions involving black holes.
