Since the discovery of low-ionization nuclear emission-line regions (LINERs
) in many galaxies, it has been recognized that they constitute a class of
active galactic nuclei (AGNs) that are thought to be powered by gas accreti
on onto a central, supermassive black hole. LINERs are observed in approxim
ately one-third of galaxies in the local universe, and it has been often th
ought that they harbor an AGN-like central engine with moderate activity. H
owever, some LINERs show no direct evidence for AGNs, such as broad emissio
n lines, radio jets, hard X-ray emission, spectral energy distributions tha
t are inconsistent with those of starlight, and so on. For such LINERs (a s
ubset of type 2 LINERs), we present new poststarburst models that explain s
ome of their most important optical narrow emission line ratios. In these m
odels, the ionization sources are planetary nebula nuclei (PNNs) with tempe
rature of similar to 10(5) K that appear in the late-phase evolution of int
ermediate-mass stars with mass between approximate to 3 and approximate to
6 M-circle dot. Such PNNs left in a typical starburst nucleus can produce a
n H alpha luminosity of L(H alpha) similar to 10(38) ergs s(-1) for typical
poststarburst LINERs and similar to 10(39) ergs s(-1) only in exceptionall
y bright cases. The PNN phase lasts until the death of the lowest-mass star
s formed in the starburst, which is similar to 5 x 10(8) yr for an assumed
lower limit of the initial mass function of 3 M-circle dot. This long durat
ion appears consistent with the observed higher frequency of occurrence of
LINERs if every galaxy could experience the starburst activity several time
s in its life. We therefore propose that some LINERs that show no direct ev
idence for AGNs may be poststarburst nuclei powered by a cluster of PNNs.