  The converging mechanism discussed in [Damour & Nordtvedt, Physical Review
Letters,70,15] for scalar-tensor theories has been applied to dilaton-like
theories in several subsequent papers. In the present communication, we show
that an unfortunate assumption in those studies led to a scalar-field equation
unsuitable for the study of the dilaton field. The corrected scalar-field
equation turns to change the numerical outcome of those studies in general, but
even sometimes their qualitative aftermath. Therefore, the present result call
for new investigations of the subject. On the other hand, our result shows that
the string-inspired theory presented in [Minazzoli & Hees, Physical Review
D,88,4] is naturally solution to the problem of the effective constancy of the
fundamental coupling constants at late cosmic times, while it requires less
fine-tuning than other massless dilaton or usual stalar-tensor theories.
