  String-loop effects may generate very weak matter couplings for a (massless)
dilaton. We examine limits on the shift of such a dilaton toward its present
equilibrium value from big-bang nucleosynthesis and the binary pulsar. On the
other hand, the approach of the dilaton toward its present value can be
realized in the early universe in a quick and efficient way if an inflationary
period is present. We comment briefly on some implications.
