  We present a method for constraining the evolution of the galaxy
luminosity-velocity (LV) relation in hierarchical scenarios of structure
formation. The comoving number density of dark-matter halos with circular
velocity of 200 km/s is predicted in favored CDM cosmologies to be nearly
constant over the redshift range 0<z<5. Any observed evolution in the density
of bright galaxies implies in turn a corresponding evolution in the LV
relation. We consider several possible forms of evolution for the zero-point of
the LV relation and predict the corresponding evolution in galaxy number
density. The Hubble Deep Field suggests a large deficit of bright (M_V < -19)
galaxies at 1.4 < z < 2. If taken at face value, this implies a dimming of the
LV zero-point by roughly 2 magnitudes. Deep, wide-field, near-IR selected
surveys will provide more secure measurements to compare with our predictions.
