  The census of young moving groups in the solar neighborhood is significantly
incomplete in the low-mass regime. We have developed a new selection process to
find these missing members based on the GALEX All-Sky Imaging Survey. For stars
with spectral types >K5 and younger than 300~Myr, we show that near-UV and
far-UV emission is greatly enhanced above the quiescent photosphere, analogous
to the enhanced X-ray emission of young low-mass stars seen by ROSAT but
detectable to much larger distances with GALEX. By combining GALEX data with
optical (HST Guide Star Catalog) and near-IR (2MASS) photometry, we identified
an initial sample of 34 young M dwarf candidates in a 1000 sq.~deg.~region
around the 10-Myr TW Hydra Association (TWA). Low-resolution spectroscopy of 30
of these found 16 which had H_alpha in emission, which were then followed-up at
high resolution to search for spectroscopic evidence of youth and to measure
radial velocities. Four objects have low surface gravities, photometric
distances and space motions consistent with TWA, but the non-detection of Li
indicates they may be too old to belong to this moving group. One object (M3.5,
93 pc) appears to be the first known accreting low-mass member of the 15~Myr
Lower Centaurus Crux OB association. Two objects exhibit all the
characteristics of the known TWA members, and thus we designate them as TWA 31
(M4.2, 110 pc) and TWA 32 (M6.3, 53 pc). TWA 31 shows extremely broad (447
km/s) H_alpha emission, making it the sixth member of TWA found to have ongoing
accretion. TWA 32 is resolved into a 0.6" binary in Keck laser guide star
adaptive optics imaging. Our search should be sensitive down to spectral types
of at least M4-M5 in TWA and thus the small numbers of new member is puzzling.
This may indicate TWA has an atypical mass function or that the presence of Li
may be too restrictive a criteria for selecting young low-mass stars.
