We have measured redshifts in the fields of the 31 R greater-than-or-e
qual-to 1 Abell clusters with 0.02 less-than-or-equal-to z less-than-o
r-equal-to 0.005 and Absolute value of b(II) > 30-degrees At least ten
of the fields are severely contaminated by superimposed velocity peak
s. We derive the mean velocities and velocity dispersions of the 25 de
nse peaks in the sample. The abundance of peaks, 6.6 x 10(-6)h3 Mpc-3,
is consistent with the mean number density of R greater-than-or-equal
-to 1 Abell clusters {Bahcall & Soneira [ApJ, 270, 20 (1983)]}. The ra
nge of velocity dispersions is 304-1346 km s-1. The median dispersion
is 718 km s-1. The subset of eight systems with cD galaxies has a medi
an velocity dispersion of 792 km s-1, close to that of non-cD systems
(626 km s-1). When these data are combined with 16 cD cluster velocity
dispersions from our previous study {Zabludoff et al. [ApJS, 74, 1 (1
990) (ZHG)] and Dunn [Proceedings of NATO Conference (1991)]), eight o
f 25 cD galaxies have peculiar motions larger than half the cluster ve
locity dispersions. These findings further support the conclusions of
Beers & Geller [ApJ, 274, 491 (1983)], ZHG, and Dunn (1991), who argue
that cD galaxies do not lie in the global kinematic center, but in lo
cal potential minima. If so, systems with speeding cD's are probably a
guide to substructure in dynamically evolving systems.