Cu2+-doped Cs2CO3 and CsHCO3 single crystals were investigated by electron paramagnetic resonance between 113-273 and 173-313K, respectively. For both single crystals, two sites were observed for the Cu2+ at ambient temperature for arbitrary orientations of the single crystals in the magnetic field. However, when the temperature is varied, the spectra indicate the equivalence of the two sites at 225 and 240K for the single crystals, respectively, to the above order. Below and above these temperatures two sites for Cu2+ appear, and below 133 and 173K the signals do not vary and two sites were always observed. This is attributed to the transition of the dynamic Jahn-Teller effect to a static situation at lower temperatures. Cu2+ seems to replace Cs+ and the charge compensation is fulfilled by another Cs+. Spin-Hamiltonian parameters for both single crystals at ambient temperature are reported and discussed.