We consider Non Autonomous Conformal Iterative Function Systems (NACIFS)and their limit set. Our main concern is harmonic measure and its dimensions : Haus-dorff and Packing. We prove that this two dimensions are continuous under perturba-tions and that they verify Bowen’s and Manning’s type formulas. In order to do so weprove general results about measures, and more generally about positive functionals,defined on a symbolic space, developing tools from thermodynamical formalism in anon-autonomous setting.