The thermodynamic equilibrium which exists between crystalline and amorphous polymeric phases is discussed in terms of a fringed micelle model, as indicated by x-ray data. An expression derived for the melting point of a crystalline polymer is found to depend on the proportion θ of amorphous material in the structure: this unsharp melting point depends ultimately on a nonlinear relationship between θ and the free energy of the system. Calculated values of the crystalline amorphous equilibrium ratio over a range of temperature are in good agreement with experimental data. An attempt has been made to extend the calculations to the case of stretched polymers and a qualitative agreement has been found. This work has been carried out in the Department of Colloid Science, Cambridge, and we should like to thank Professor E. K. Rideal for much stimulating criticism. This paper arose out of discussions with Professor Sir R. H. Fowler: his advice and encouragement during its development have been invaluable to us, and we should like to record here our grateful thanks to him.