A reconstruction strategy is proposed for physiological motion correction, which overcomes many limitations of existing techniques. The method is based on a general framework allowing correction for arbitrary motion-nonrigid or affine, making it suitable for cardiac or abdominal imaging, in the context of multiple coil, arbitrarily sampled acquisition. A model is required to predict motion in the field of view at each sample time point, based on prior knowledge provided by external sensors. A theoretical study is carried out to analyze the influence of motion prediction errors. Small errors are shown to propagate linearly in that reconstruction algorithm, and thus induce a reconstruction residue that is bounded (stability). Furthermore, optimization of the motion model is proposed in order to minimize this residue. This leads to reformulating reconstruction as two inverse problems which are coupled: motion-compensated reconstruction (known motion) and model optimization (known image). A fixed-point multiresolution scheme is described for inverting these two coupled systems. This framework is shown to allow fully autocalibrated reconstructions, as coil sensitivities and motion model coefficients are determined directly from the corrupted raw data. The theory is validated with real cardiac and abdominal data from healthy volunteers, acquired in free-breathing.