  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 streaming, 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% of the circular
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.
