| Galactic nuclei are sites of intense activity, harboring super-starclusters, galactic winds and even supermassive black holes. Since stars form from molecular gas, a complete understanding of starburst galaxies is impossible without a detailed understanding of the nature of the molecular gas in these objects. In this thesis I study the molecular gas in the nuclear regions four nearby, actively star forming galaxies: IC 342, Maffei 2, NGC 6946 and NGC 4826, to measure the masses, locations, temperatures and densities of the gas and its correlation with the ongoing star formation. I employ high resolution (∼50 parsecs) images of the two lowest rotational transitions (J = 2-1, 1-0) of carbon monoxide and its isotopomers (12CO, 13CO, C18O) obtained with the Owens Valley Millimeter Array. Continuum fluxes at 1.4 and 2.7 millimeters are used to characterize the dust properties and star formation strengths.; The main results of this thesis include the following. (1) The physical conditions of these galactic nuclei are quite similar to those found in the center of our Galaxy. Gas excitation varies significantly on individual molecular cloud scales, often in decidedly non-LTE ways. (2) While star formation favors regions containing the densest gas, the star formation appears to be driven by the dynamics of the nuclear region and not by gas density. The observed dynamical forces can be particularly sensitive to small scale changes in the nuclear stellar mass distribution. (3) Use of a "Galactic conversion factor", XCO, between 12CO(1-0) intensity and molecular gas column density leads to significant overestimates of the amount of molecular gas in these galactic nuclei and presumably all nuclei. XCO varies from galaxy to galaxy and within each galaxy, but is not directly related to the physical conditions of the gas. In addition to CO, seven other molecules---C2H, HNCO, HNC, HC3N, C34S, CH3OH, N2H +---were mapped in the nuclear minispiral of IC 342. The differences in morphology among these species indicate that, surprisingly, the gas chemistry varies significantly across the nucleus, even on 100 pc sizescales. |