Accurate demagnetization modelling is mandatory for a reliable design of rare-earth permanent magnet applications, such as e.g. synchronous machines. The magnetization of rare-earth permanent magnets requires high magnetizing fields. For technical reasons, it is not always possible to completely and homogeneously achieve the required field strength during a pulse magnetization, due to stray fields or eddy currents. Not sufficiently magnetized magnets lose remanence as well as coercivity and the demagnetization characteristic becomes strongly nonlinear. It is state of the art to treat demagnetization curves as linear. This paper presents an approach to model the nonlinear demagnetization in dependence on the magnetization field strength. Measurements of magnetization dependent demagnetization characteristics of rare-earth permanent magnets are compared to an analytical model description. The physical meaning of the model parameters and the influence on them by incomplete magnetization are discussed for different rare-earth permanent magnet materials. Basically, the analytic function is able to map the occurring magnetization dependent demagnetization behavior. However, if the magnetization is incomplete, the model parameters have a strong nonlinear behavior and can only be partially attributed to physical effects. As a benefit the model can represent nonlinear demagnetization using a few parameters only. The original analytical model is from literature but has been adapted for the incomplete magnetization. The discussed effect is not sufficiently accurate modelled in literature. The sparse data in literature has been supplemented with additional pulsed-field magnetometer measurements.