We present the derived kinematic characteristics of low-α thin-disk and high-α thick-disk stars in the Milky Way, investigated with a sample of about 32,000 G- and K-type dwarfs from the Sloan Extension for Galactic Understanding and Exploration (SEGUE). Based on the level of α-element enhancement as a function of [Fe/H], we separate our sample into thin- and thick-disk stars and then derive mean velocities, velocity dispersions, and velocity gradients for the U, V, and W velocity components, respectively, as well as the orbital eccentricity distribution. There are notable gradients in the V velocity over [Fe/H] in both populations: −23 km s−1 dex−1 for the thin disk and +44 km s−1 dex−1 for the thick disk. The velocity dispersion of the thick disk decreases with increasing [Fe/H], while the velocity dispersion gradient over [Fe/H] for the thin disk is almost flat for all velocity components, except for the W velocity dispersion of the metal-poor thin-disk stars. The eccentricity distribution exhibits a peak at a higher value, and is more symmetric as [α/Fe] increases, implying that complex formation mechanisms may be involved. Our results can be used to constrain several proposed disk-formation scenarios of the Milky Way and other large spirals.