NMR data are presented for the conducting delafossites Y0.99Ca0.01CuO2
.65 and LaCuO2.64. These materials exhibit a planar structure with tri
angular arrays of exchange-coupled S = 1/2 (Cu2+) spins. The two compo
unds examined show strikingly different quadrupole-broadened NMR powde
r patterns, which is evidence for different in-plane arrangements of O
2- ions. Their doped-hole carrier densities are comparable to those of
the superconducting cuprates. In consequence, they have Korringa-like
T1 processes. We, also find evidence for dynamic Jahn-Teller motion a
nd ferromagnetic enhancement of the spin paramagnetism for Y0.99Ca0.01
CuO2.65. T2 studies indicate that the strong antiferromagnetic fluctua
tion effects found in the superconducting cuprates are absent.