Abstract. The statistical and dynamical properties of bias correction and linear post-processing are investigated when the system under interest is affected by model errors and is experiencing parameter modifications, mimicking the potential impact of climate change. The analysis is first performed for simple typical scalar systems, an Ornstein-Uhlenbeck process (O-U) and a limit point bifurcation. It reveals system's specific (linear or non-linear) dependences of biases and post-processing corrections as a function of parameter modifications. A more realistic system is then investigated, a low-order model of moist general circulation, incorporating several processes of high relevance in the climate dynamics (radiative effects, cloud feedbacks...), but still sufficiently simple to allow for an extensive exploration of its dynamics. In this context, bias or post-processing corrections also display complicate variations when the system experiences temperature climate changes up to a few degrees. This precludes a straightforward application of these corrections from one system's state to another (as usually adopted for climate projections), and increases further the uncertainty in evaluating the amplitudes of climate changes.