  A moderate resolution spectroscopic survey of Fleming's sample of 54 X-ray
selected M dwarfs with photometric distances less than 25 pc is presented.
Radial and rotation velocities have been measured by fits to the H-alpha
profiles. Radial velocities have been measured by cross correlation. Artificial
broadening of an observed spectrum has produced a relationship between H-alpha
FWHM and rotation speed, which we use to infer rotation speeds for the entire
sample by measurement of the H-alpha emission line. We find 3 ultra-fast
rotators (UFRs, vsini > 100km/s), and 8 stars with 30 < vsini < 100 km/s. The
UFRs have variable emission. Cross-correlation velocities measured for
ultra-fast rotators (UFRs) are shown to depend on rotation speed and the
filtering used. The radial velocity dispersion of the sample is 17 km/s. A new
double emission line spectroscopic binary with a period of 3.55 days has been
discovered, and another known one is in the sample. Three other objects are
suspected spectroscopic binaries, and at least six are visual doubles. The only
star in the sample observed to have significant lithium is a known TW Hya
Association member, TWA 8A. These results show that there are a number of young
(< 10^8 yr) and very young (< 10^7 yr) low mass stars in the immediate solar
neighbourhood. The H-alpha activity strength does not depend on rotation speed.
Our fast rotators are less luminous than similarly fast rotators in the
Pleiades. They are either younger than the Pleiades, or gained angular momentum
in a different way.
