Biaxial order in free-standing films of poly(ecaprolactone) (PCL), induced by plastic deformation and fibrillation, is studied by infrared transition moment orientational analysis (IR-TMOA) and X-ray diffraction (pole figures). This enables one to determine the order parameter tensor for the different molecular moieties with respect to the sample coordinate system. The main chains of the polymers are aligned with the stretching direction (x) under bar, leading to a strong order of the crystallites (Hermans orientation function, S-xx = 0.9 +/- 0.1), and less ordered, amorphous regions (S-xx = 0.34 +/- 0.1). The microscopic biaxiality of the system, vertical bar S-yy S-zz vertical bar approximate to 0.1, is caused by the macroscopically asymmetric deformation perpendicular to the stretching direction. Cold drawing leads to a reduction in crystallinity and distorted crystallites in the fibrils, indicating the absence of "melting and recrystallization" or "fine slip" processes.