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The noise of YBa2Cu3O7-χ and Ti2Ba2Ca2Cu2O10-χ thin films in the frequency range from 0.5 Hz to 100 kHz was studied. In the normal state, it was found that 1/f noise dominated, with a magnitude strongly dependent on temperature. In the superconducting state, the noise was only observable at frequencies below 5 Hz with our present setup. Equilibrium thermal fluctuation noise was not observed in these films.