  Precision comparisons of different atomic frequency standards over a period
of a few years can be used for a sensitive search for temporal variations of
fundamental constants. We present recent frequency measurements of the 688 THz
transition in the $^{171}$Yb$^+$ ion. For this transition frequency a record
over six years is now available, showing that a possible frequency drift
relative to a cesium clock can be constrained to $(-0.54\pm0.97)$ Hz/yr, i.e.
at the level of $2\cdot10^{-15}$ per year. Combined with precision frequency
measurements of an optical frequency in $^{199}$Hg$^+$ and of the hyperfine
ground state splitting in $^{87}$Rb a stringent limit on temporal variations of
the fine structure constant $\alpha$: $d\ln\alpha /dt= (-0.26\pm0.39)\cdot
10^{-15} {\rm yr}^{-1}$ and a model-dependent limit for variations of the
proton-to-electron mass ratio $\mu$ in the present epoch can be derived: $d \ln
\mu/dt = (-1.2 \pm 2.2)\cdot 10^{-15} {\rm yr}^{-1}$. We discuss these results
in the context of astrophysical observations that apparently indicate changes
in both of these constants over the last 5--10 billion years.
