To examine the role of the host galaxy structure in fueling nuclear activity, we estimated gas flow rates from several kpc down to the inner few 10 pc for seven nearby spiral galaxies, selected from the NUclei of GAlaxies sample. We calculated gravitational torques from near-infrared images and determined gas in/out-flow rates as a function of radius and location within the galactic disks, based on high angular resolution interferometric observations of molecular (CO using Plateau de Bure interferometer) and atomic (H I using the Very Large Array) gas. The results are compared with kinematic evidence for radial gas flows and the dynamical state of the galaxies (via resonances) derived from several different methods. We show that gravitational torques are very efficient at transporting gas from the outer disk all the way into the galaxies centers at ~100 pc; previously assumed dynamical barriers to gas transport, such as the corotation resonance of stellar bars, seem to be overcome by gravitational torque induced gas flows from other nonaxisymmetric structures. The resulting rates of gas mass inflow range from 0.01 to 50 M⊙ yr^(–1) and are larger for the galaxy center than for the outer disk. Our gas flow maps show the action of nested bars within larger bars for three galaxies. Noncircular streaming motions found in the kinematic maps are larger in the center than in the outer disk and appear to correlate only loosely with the in/out-flow rates as a function of radius. We demonstrate that spiral gas disks are very dynamic systems that undergo strong radial evolution on timescales of a few rotation periods (e.g., 5 × 10^8 yrs at a radius of 5 kpc), due to the effectiveness of gravitational torques in redistributing the cold galactic gas