  We show that a multilayer analysis of the infrared c-axis response of
RBa2Cu3O7-d (R=Y, Gd, Eu) provides important new information about the
anomalous normal state properties of underdoped cuprate high temperature
superconductors. Besides competing correlations which give rise to a pseudogap
that depletes the low-energy electronic states below T*>>Tc, it enables us to
identify the onset of a precursor superconducting state below Tons>Tc. We map
out the doping phase diagram of Tons which reaches a maximum of ~180 K at
strong underdoping and present magnetic field dependent data which confirm our
conclusions.
