  We make use of the comparison between measurements of various pairs of atomic
clocks to impose constraints on coupled variations of fundamental constants in
severs unification scenarios. We obtain null results for the proton-to-electron
mass ratio ${\dot\mu}/{\mu}=(0.68\pm5.79)\times10^{-16}\, {\rm yr}{}^{-1}$ and
for the gyromagnetic factor ${\dot g_p}/{g_p}=(-0.72\pm0.89)\times10^{-16}\,
{\rm yr}{}^{-1}$ (both of these being at the 95% confidence level). These
results are compatible with theoretical expectations on unification scenarios
(which we briefly describe), but much freedom exists due to the presence of a
degeneracy direction in the relevant parameter space.
