The crystallization of natural and glass fibre reinforced poly(propylene) (PP) and poly(butylene terephthalat) (PBT) has been investigated during very fast cooling (dT/dt < 200 K/s) and under pressure (p < 200 MPa). For this, an apparatus for quenching has been designed which features boundary conditions that are comparable to the injection moulding process and at the same time well defined. This allows for the treatment of heat conduction as being one-dimensional. The equations governing crystallization kinetics are based on nucleation and growth and include a pressure dependance. The thermal material data are described with regards to the morphology (glass fibre content, ...). The model has been implemented into a finite-differences-scheme to compute the temperature distribution, the degree of crystallinity and the material data. Furthermore, it is possible to predict the resulting morphology. The investigations are accomplished by a comparison between measured and calculated values as well as studies of parameter variations.