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 .
All the objects consist of one or two dMe stars , some being doubles or spectroscopic binaries .
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 , v \sin i \geq 100 km s ^ { -1 } ) , and 8 stars with 30 km s ^ { -1 } \leq v \sin i < 100 km s ^ { -1 } .
We find that the UFRs have quite variable emission and should be observed for photometric variability .
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 ^ { -1 } .
A new double emission line spectroscopic binary with a period of 3.55 days has been discovered , RX J1547.4+4507 , and another known one is in the sample , the Hyades member RX J0442.5+2027 .
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 happens to be a known TW Hya Association member , TWA 8A .
These results all 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 .