Motivated by the discovery of young, massive stars in the nuclei of some LINER/H II ``transition nuclei such as NGC 4569, we have computed photoionization models to determine whether some of these objects may be powered solely by young star clusters rather than by accretion-powered active nuclei. The models were calculated with the photoionization code CLOUDY, using evolving starburst continua generated by the the STARBURST99 code of Leitherer et al. (1999). We find that the models are able to reproduce the emission-line spectra of transition nuclei, but only for instantaneous bursts of solar or higher metallicity, and only for ages of ~3-5 Myr, the period when the extreme-ultraviolet continuum is dominated by emission from Wolf-Rayet stars. For clusters younger than 3 Myr or older than 6 Myr, and for models with a constant star-formation rate, the softer ionizing continuum results in an emission spectrum more typical of H II regions. This model predicts that Wolf-Rayet emission features should appear in the spectra of transition nuclei. While such features have not generally been detected to date, they could be revealed in observations having higher spatial resolution. Demographic arguments suggest that this starburst model may not apply to the majority of transition nuclei, particularly those in early-type host galaxies, but it could account for some members of the transition class in hosts of type Sa and later. The starburst models during the Wolf-Rayet-dominated phase can also reproduce the narrow-line spectra of some LINERs, but only under conditions of above-solar metallicity and only if high-density gas is present (n_e >~ 10^5 cm^{-3}). This scenario could be applicable to some ``Type 2 LINERs which do not show any clear signs of nonstellar activity.
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