We present the results of a multiwavelength investigation of energy generation mechanisms in 33 objects from the IRAS Bright Galaxy Sample. This study is based on long-slit optical spectroscopy and near-infrared broadband imaging at J, H, and K. We used established emission-line criteria, involving [O III] λ5007/Hβ, [N II λ6583/Hα, [S II] (λ6716 + λ6731)/Hα, and [O I] λ6300/Hα intensity ratios, to classify the optical spectra of all 36 sample nuclei (three sources were binary systems). The line ratios indicate that our sample contains seven active galactic nuclei (AGNs) and 24 starburst galaxies. We also find that five galaxies (straddlers) cannot be straightforwardly classified by this simple scheme. Follow-up near-infrared imaging of the straddler galaxies yields near-infrared colors consistent with emission from relatively weak AGNs. Considered together with the fact that their narrow optical emission-line ratios resemble those of NGC 7469, which is known to contain an unresolved AGN inside an H II region-like galaxy disk or torus, the evidence seems to indicate that NGC 7469 may be typical of a pattern exhibited by infrared luminous galaxies, i.e., that low-luminosity AGNs and starbursts often coexist in infrared-selected galaxies.