M any polymeric materials crystallize when cooled below their melting temperature. Although progress has been made in our understanding of the crystallization process through both experimental(1) and theoretical(2-6) efforts, these studies have focused mainly on the crystal nucleation and growth mechanism, where critical nuclei are formed from a metastable state during the first stages of crystallization, leading ultimately to the growth of crystal domains. Attention has also been given to the structure during the precrystallization (induction period(7-13)). A pretransition state occurring before crystallization has been characterized as an unstable phase separation initiated by density and orientational fluctuations. These fluctuations are caused by an increase in the average length of rigid trans segments along the polymer backbone during the induction period. These observations are consistent with the theory proposed in ref. 14 on the isotropic-to-nematic transition of polymer liquid crystals, that is, the parallel ordering of polymers is caused by an increase in chain rigidity. Here we use large-scale computer simulations to investigate melts of polymers in the early ordering stages (induction period) before crystallization. In the ordered domains we identify growing dense regions similar to smectic liquid crystals. Our simulations reveal a 'coexistence period' in the ordering before crystallization, where nucleation and growth mechanisms coexist with a phase-separation mechanism.