We present two-dimensional Hα velocity fields for ten well-defined nuclear rings observed with the DensePak fiber-optic array on the KPNO WIYN telescope. In this paper, we present detailed results for two of those rings, in NGC 1530 and NGC 4314. We conclude that in general regions of enhanced Hα, thus massive star formation, in the nuclear rings correspond to regions with (1) high luminosities, of order 1040-1042 erg s-1, (2) low residual velocities, after subtracting disk rotation, of order 10 km s-1, and (3) low velocity dispersions in the range 20-50 km s-1. In the rings, star formation takes place in regions where the shear is small and the gas is cool enough to allow molecular condensation. The lack of strong non-circular motions, coupled with a direct relationship between the position angles and ellipticities of the rings and those of their host galaxies, indicates that the rings are in the same plane as the disk and are circular.