  Over five years we have compared the hyperfine frequencies of 133Cs and 87Rb
atoms in their electronic ground state using several laser cooled 133Cs and
87Rb atomic fountains with an accuracy of ~10^{-15}. These measurements set a
stringent upper bound to a possible fractional time variation of the ratio
between the two frequencies : (d/dt)ln(nu_Rb/nu_Cs)=(0.2 +/- 7.0)*10^{-16}
yr^{-1} (1 sigma uncertainty). The same limit applies to a possible variation
of the quantity (mu_Rb/mu_Cs)*alpha^{-0.44}, which involves the ratio of
nuclear magnetic moments and the fine structure constant.
