A class of generalized nonminimal coupling theories is investigated, in sea
rch of scaling attractors able to provide an accelerated expansion at the p
resent time. Solutions are found in the strong coupling regime and when the
coupling function and the potential verify a simple relation. In such case
s, which include power law and exponential functions, the dynamics is indep
endent of the exact form of the coupling and the potential. The constraint
from the time variability of G, however, limits the fraction of energy in t
he scalar field to less than 4% of the total energy density, and excludes a
ccelerated solutions at the present. [S0556-2821(99)01414-9].