We report the operation of a dual Rb/Cs atomic fountain clock. 133Cs and 87Rb atoms are cooled, launched, and detected simultaneously in LNE-SYRTEs FO2 double fountain. The dual clock operation occurs with no degradation of either the stability or the accuracy. We describe the key features for achieving such a simultaneous operation. We also report on the results of the first Rb/Cs frequency measurement campaign performed with FO2 in this dual atom clock configuration, including a new determination of the absolute 87Rb hyperfine frequency.