CO and HI velocity fields of seven nearby spiral galaxies, derived from radio-interferometric observations, are decomposed into Fourier components whose radial variation is used to search for evidence of radial gas flows. Additional information provided by optical or near-infrared isophotes is also considered, including the relationship between the morphological and kinematic position angles. To assist in interpreting the data, we present detailed modeling that demonstrates the effects of bar

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... reaming, inflow, and a warp on the observed Fourier components. We find in all of the galaxies evidence for either elliptical streaming or a warped disk over some range in radius, with deviations from pure circular rotation at the level of 20-60 km/s. Evidence for kinematic warps is observed in several cases well inside R_25. No unambiguous evidence for radial inflows is seen in any of the seven galaxies, and we are able to place an upper limit of 5-10 km/s (3-5 speed) on the magnitude of any radial inflow in the inner regions of NGC 4414, 5033 and 5055. We conclude that the inherent non-axisymmetry of spiral galaxies is the greatest limitation to the direct detection of radial inflows.