  In this note we study the 2PN/RM gauge invariance structure of a
\textit{Brans-Dicke-like} Scalar-Tensor Theories (STT) without potential. Since
the spherical isotropic metric plays an important role in the literature, its
2PN/RM STT version is deduced from the general equations given in
\cite{moiCQG11}, by using the invariance structure properties. It is found that
the second order Eddington parameter $\epsilon$ can be written in terms of the
usual post-Newtonian parameter $\gamma$ and $\beta$ as $ \epsilon=4/3 \gamma^2
+ 4/3 \beta - 1/6 \gamma -3/2$
