Low-wavenumber vibrational dynamics are studied for liquid formamide (FA) and N-methylformamide (NMF) by the methods of molecular dynamics (MD) and instantaneous normal mode (INM) analysis. The dipole-induced dipole (DID) mechanism is employed for calculating polarizability tensors, the correlation function of which determines Raman spectral profiles and optical Kerr effect (OKE) responses. It is shown that the calculated Raman spectra and OKE responses are in reasonable agreement with those observed in previous studies. The main features of these optical signals are explained by simple librations of the unperturbed molecular polarizability (UMP) tensors, which are considerably anisotropic, although the intensities of the librational components are enhanced to some extent by intermolecular interactions, especially in the case of liquid NMF, The DID term gives rise to smaller intensities in a lower wavenumber region than the UMP term. It is suggested that these features of the optical signals may be regarded as characteristic of strongly interacting liquids with substantial anisotropy in molecular polarizability tensors. It is also shown that the marked difference between the Raman spectra of liquid FA and NMF in the low-wavenumber region arises from a difference in the librations of these molecules around the longer in-plane molecular axis of inertia. The difference is related to the dimensionality of hydrogen bonding in the liquids: two-dimensional in liquid FA and one-dimensional in liquid NMF.