A macroscopic model for the description of low- and high-speed fiber spinning of crystallizing polymers is proposed. The model incorporates air drag, air cooling, gravity, surface tension and the viscoelastic rheological behavior of the melt. The crystallization dynamics are formulated through a set of rate equations, which describe the quiescent nucleation and growth of spherulites, as well as the flow-induced nucleation and longitudinal growth of fibrils. The influence of the crystallization, as well as the glass transition, on the rheological response is accounted for through a viscous stress contribution. The proposed model realistically describes the velocity, temperature, stress, apparent viscosity and crystallinity profile along the spinline under different processing conditions. Moreover, using a single set of model parameters a fair description of the experimental velocity and temperature profiles is obtained for both low- and high-speed spinning conditions of nylon 66. For poly(ethylene terephthalate) the model describes high-speed spinning conditions only.