RED-GIANT BRANCH OF THE OLD, METAL-RICH OPEN CLUSTER NGC-6791

V and I photometry out to 12' from the center of the old, populous, me tal-rich, open cluster NGC 6791 has revealed 16 bright stars (I less-t han-or-equal-to 12.5) with 1.6 less-than-or-equal-to V-I less-than-or- equal-to 4.1. Follow-up spectroscopy indicates that (1) at least 12 of these red-giant branch (RGB) candidates are bona fide cluster members , and (2) their metallicity, as estimated from the strength of the Ca II infrared triplet lines, is slightly above solar. If the core helium -burning (''clump'') stars in NGC 6791 have a mean M(V) = 0.9, which i s the current best estimate for that of their counterparts in the [M/H ] almost-equal-to 0.0 cluster M67, then the apparent distance modulus of the former is near (m-M)v almost-equal-to 13.6. This would imply an age of about 9 Gyr, from appropriate stellar models, versus almost-eq ual-to 4.5 Gyr for M67. Importantly, with this estimate of the distanc e-which is unlikely to be in error by more than +/-0.25 mag-the color- magnitude diagram (CMD) of NGC 6791 intimates that its RGB does not ri se above M(I) approximately -2.7. In contrast, the RGBs of all Galacti c globular clusters with metallicities of one-quarter solar or less ar e presently believed to reach M(I) almost-equal-to -4.0, though fainte r tip magnitudes have been inferred for the very few globulars of high er metal abundance (e.g., NGC 6553) that have been studied. If the tip M(I) value does vary with metallicity among (at least) the most metal -rich systems, then that variation can be expected to affect, e.g., es timates of the extragalactic distance scale based on the ''surface bri ghtness fluctuation'' method. Consequently, NGC 6791 provides an excee dingly important constraint on our understanding of old, metal-rich st ellar populations. Encouragingly, theoretical evolutionary tracks whos e temperatures and colors are consistent with various empirical constr aints appear to provide a fine match to the upper CMD of NGC 679 1, if the cluster metallicity is [M/H] > 0.0.