We show that the one-particle spectral functions of the one-dimensiona
l Hubbard model diverge at the Fermi energy like \omega - epsilon(F)\(
-3/8) in the U --> + infinity limit. The Luttinger liquid behavior to
\omega - epsilon(F)\(alpha), where alpha --> 1/8 as U --> + infinity,
should be limited to \omega - epsilon(F)\ similar to t(2)/U (for U lar
ge but finite), which shrinks to a single point, omega = epsilon(F), i
n that limit. The consequences for the observation of the Luttinger li
quid behavior in photoemission and inverse photoemission experiments a
re discussed.