I present a spectroscopic study of the molecular gas in the Whirlpool Galaxy (M51) and the Antennae Galaxies (NGC 4038/39) using data from the Herschel Space Observatory (Herschel) and the Atacama Large Millime- ter/submillimeter Array (ALMA). Using data from the Herschel Spectral and Photometric Imaging REceiver (SPIRE) Fourier Transform Spectrometer (FTS), I perform an excitation analysis to determine the physical characteris- tics (temperature, density, column density) of the cold and warm molecular gas across both systems. I do not find significant variation in the cold molecular gas across an individual system or between the systems. The warm molecular gas temperature is greater in NGC 4038/39 than in M51, while the density in both M51 and the nucleus of NGC 4038 is greater than the rest of the Anten- nae system. Both galaxies exhibit a similar fraction of warm to cold molecular gas. I compare Herschel SPIRE-FTS data to models of photon dominated regions (PDRs) to determine the strength of the background far ultraviolet field (G0) within both systems and find little variation across each system. I find that PDRs alone can explain the observed Herschel SPIRE-FTS data in both systems. Using ALMA observations of dense molecular gas tracers in NGC 4038/39, I investigate the physical processes affecting the dense molecular gas. Ratios of various molecular gas tracers suggest that the contributions of mechanical heating relative to PDR heating are similar across the entire system. The dense gas fraction in the nucleus of NGC 4038 and the nucleus of NGC 4039 is higher than in the overlap region, which I attribute to an increase in the stellar potential within the two nuclei. Furthermore, I find evidence for an increased cosmic ray rate in the overlap region of NGC 4038/39 relative to the two nuclei, which I attribute to an increased supernova rate in the overlap region. Most of the molecular gas in M51 and NGC 4038/39 is in the form of PDRs, while the increased temperature of the warm molecular gas in NGC iii 4038/39 compared to M51 is likely due to an increase in the mechanical heating from both supernova and stellar winds and the ongoing merger. Furthermore, a comparison of these results to previous studies of the interacting galaxy M82 and the late-stage merger Arp 220 suggests that mergers and interactions have a greater effect on the warm molecular gas compared to the cold molecular gas. The results from this thesis help to further our understanding of the effects of merging and interacting galaxies on molecular gas, while helping understand differences between interacting galaxies and merging galaxies. / Thesis / Doctor of Philosophy (PhD)