without, however, including the additional terms represented there by “more”. We then give some general rules for computing the subcritical domain of the dilaton couplings guaranteeing velocity-dominance (section \[subcritical\]). The inclusion of interaction terms is considered in the last sections. It is shown that they do not affect the asymptotic analysis. This is done first for the Chern-Simons and Chapline-Manton interactions in section \[couple\], and next, in section \[yangmills\], for the Yang-Mills couplings (for some gauge group $G$), for which the action reads $$\label{actionym}
S[g_{\alpha \beta}, \phi, A_\gamma] =
{1 \over 2} \int \{ R - \partial_\mu \phi \, \partial^\mu \phi
- {1 \over 2} F_{\mu \nu} \cdot F^{\mu \nu} e^{\lambda \phi} \}
\sqrt{-g} \, d^D x.$$ Here the dot product, $F \cdot F$, is a time-independent, Ad-invariant, non-degenerate scalar product on the Lie algebra of $G$ (such a scalar product exists if the algebra is compact, or semi-simple). Contrary to what is done in sections \[scaMax4D\], \[nform\] and \[couple\], we must work now with the vector potential (and not just with the field strength), since it appears explicitly in the coupling terms. In section \[nonlinear\] we show that self-interactions of a rather general type for the scalar field can 