  Two first order strongly hyperbolic formulations of scalar-tensor theories of
gravity (STT) allowing nonminimal couplings (Jordan frame) are presented along
the lines of the 3+1 decomposition of spacetime. One is based on the Bona-Masso
formulation while the other one employs a conformal decomposition similar to
that of Baumgarte-Shapiro-Shibata-Nakamura. A modified Bona-Masso slicing
condition adapted to the scalar-tensor theory is proposed for the analysis.
This study confirms that the scalar-tensor theory posses a well posed Cauchy
problem even when formulated in the Jordan frame.
