Since the discovery of low-ionization nuclear emission-line regions in many galaxies (LINERs), it has been recognized that they constitute a class of active galactic nuclei (AGNs) which are thought to be powered by gas accretion onto a central, supermassive black hole. LINERs are observed in approximately one third of galaxies in the local universe and it has been often thought that they harbor an AGN-like central engine with moderate activity. However, some LINERs show no direct evidence for AGNs such as broad emission lines, radio jets, hard X-ray emission, spectral energy distributions which are inconsistent with starlight, and so on. For such LINERs (a subset of type 2 LINERs), we present new poststarburst models which explain some of their most important optical narrow emission-line ratios. In these models, the ionization sources are planetary nebula nuclei (PNNs) with temperature of ~ 10^5 K which appear in the late-phase evolution of intermediate-mass stars with mass between ~ 3 M_solar and ~ 6 M_solar. Such PNNs left in a typical starburst nucleus can produce an Halpha luminosity of L(Halpha) ~ 10^38 ergs s^-1 for typical poststarburst LINERs and ~ 10^39 ergs s^-1 only in exceptionally bright cases. The PNN phase lasts until the death of the lowest-mass stars formed in the starburst, which is ~ 5 x 10^8 yr for an assumed lower limit of the initial mass function of 3 M_solar. This long duration appears consistent with the observed higher frequency of occurrence of LINERs if every galaxy could experience the starburst activity several times in its life. We therefore propose that some LINERs which show no direct evidence for AGNs may be poststarburst nuclei powered by a cluster of PNNs.

8 pages, 6 figures, emulateapj.sty; To appear in the September 2000 issue of the Astronomical Journal