This paper reports the results of a near infrared spectroscopic survey of LINER galaxies undertaken with a new infrared spectrograph at the 5 m Hale telescope. The galaxy sample includes 11 LINERs with spectra covering the [FeII] (1.2567 microns), PaBeta (1.2818 microns), H2 (1-0 S(1), 2.1218 microns) and BrGamma (2.1655 microns) near infrared emission lines, and one additional galaxy with only [FeII] and Pa$beta$ line coverage. All of the LINERs with infrared line detections have strong [FeII] and/or H2 emission, with about half (4 out of 9) having extremely high ratios (>2) of [FeII] to PaBeta. The strength of the H2 and [FeII] lines is well correlated with the optical [OI] line, with many LINERs having higher ratios of [FeII]/PaBeta, H2/BrGamma and [OI]/H-Alpha than other galaxy types. The LINERs with the highest [FeII]/PaBeta ratios (termed ``strong [FeII] LINERs) show evidence for recent star formation. Shocks from compact supernova remnants may enhance the [FeII] emission in these ``strong [FeII] LINERs. The LINERs with lower [FeII]/PaBeta ratios (termed ``weak [FeII] LINERs) are more consistent with Seyfert-like activity, including higher ionization states, some strong x-ray sources and some broad H-Alpha detections. The [FeII] luminosity and the [FeII]/PaBeta ratio in these objects are more easily explained by hard x-ray excitation than in the ``strong [FeII] LINERs. These ``weak [FeII] LINERs are considered prime candidates for being low luminosity Seyfert nuclei.
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