  We present the results of a long-slit K-band spectroscopic search with CGS4
on UKIRT for H-alpha emission from the objects responsible for high-redshift (z
> 2) damped Ly-alpha absorption systems. The objective was to measure the
star-formation rates in these systems. However, no H-alpha emission was
detected above our 3-sigma limits of f < 10E-19 W/m**2, corresponding to star
formation rates < 10 M_sun/yr/h**2 (q_0=0.5). These upper limits are more
meaningful than those from searches for Ly-alpha emission because the H-alpha
line is unaffected by resonant scattering. For q_0=0.5 our limits are in
conflict with the star formation rates predicted under the assumption that the
high-z DLAs are the fully-formed galactic-disk counterparts of today's massive
spiral galaxies. Deeper spectroscopy is needed to test this picture for
q_0=0.0. A programme of NICMOS imaging observations currently underway,
combined with VLT spectroscopy, will provide a detailed picture of the link
between DLAs and young galaxies.
