We report high S/N (> 2000), high-resolution (almost-equal-to 1 km s-1
) observations of the interstellar Li I absorption lines toward the st
ars zeta Oph and zeta Per. Our Li I line profiles indicate the presenc
e of both the Li-7 (lambda(rest) = 6707.761, 6707.912 angstrom) and Li
-6 (6707.921, 6708.072 angstrom) doublets in these two sightlines. The
resultant best-fit values (using a single-component profile) for the
interstellar Li-7/Li-6 isotope ratio are 6.8 (+ 1.4, - 1.7) toward zet
a Oph and 5.5 (+ 1.3, - 1.1) toward zeta Per. It is clear from our dat
a that the Li-7/Li-6 ratio toward zeta Oph and zeta Per is less than t
he meteoritic value (12.6) representative of the early solar system. T
his result does not support the lower limit of 25 set for the interste
llar Li-7/Li-6 ratio by Ferlet & Dennefeld from their Li I observation
s toward zeta Oph. However, our findings agree much better with the re
cent Li-7/Li-6 measurement of 12.5 (+ 4.3, - 3.4) toward rho Oph by Le
moine et al. Since current models of Galactic chemical evolution predi
ct that the Li-7/Li-6 ratio should increase with time, these new resul
ts suggest that the production of Li-6 is being enhanced through cosmi
c-ray spallation or some other process.