The application of the Cartesian coordinate tensor transfer (CCT) technique for simulations of the IR absorption and vibrational circular dichroism (VCD) spectra of relatively large nucleic acid fragments is demonstrated on several case studies. The approach is based on direct ab initio calculations of atomic tensors, determining molecular properties, for relatively small fragments, and subsequent transfer of these tensors to the larger systems in Cartesian coordinates. This procedure enables precise computations of vibrational spectra for large biomolecular systems, currently with up to several thousands of atoms. The versatile ability of the CCT methods is emphasized on the examples of VCD and IR absorption spectra calculations for B- and Z-forms of DNA, single-, double-, and triple-stranded RNA helices and DNA structures with different base content and sequences. The development and recent improvements of the methodology are followed, including utilization of the constrained normal mode optimization (NMO) strategy and combined quantum mechanics and molecular dynamics simulations. Advantages, drawbacks, and recommendations for future improvements of the CCT method as applied to nucleic acid spectra calculations are discussed.