  Recent detections of high-redshift absorption by both atomic hydrogen and
molecular gas in the radio spectra of quasars have provided a powerful tool to
measure possible temporal and spatial variations of physical `constants' in the
Universe.
  We have compared the frequency of high-redshift Hydrogen 21 cm absorption
with that of associated molecular absorption in two quasars to place new (1
sigma) upper limits on any variation in y = g_p.alpha^2 (where alpha is the
fine structure constant and g_p is the proton g-factor) of |Delta(y)/y| <
5.10^{-6} at redshifts z=0.25 and z=0.68. These quasars are separated by a
comoving distance of 3000 Mpc (H_0=75 km/s/Mpc and q_0=0). We also derive
limits on the time rates of change of |(d.g_p/d.t)/g_p| < 10^{-15}/y and
|(d.alpha/d.t)/\alpha| < 5.10^{-16}/y between the present epoch and z=0.68.
These limits are more than an order of magnitude smaller than previous results
derived from high-redshift measurements.
