We investigated the general properties of polarization effects in optical fibres and demonstrated the existence of socalled principal states of polarization (PSP), which mean the fixed points in mathematics, in different polarization effects,such as birefringence and polarization mode dispersion, by using fixed point theory. Furthermore, a time evolution vector is defined to describe the time evolution of polarization state in optical fibres, which is used to investigate the time evolution of polarization mode dispersion vector (PDV), including differential group delay and PSP. The experimentalresults of real-time monitoring of PDV by using this method are reported. To our knowledge, this is the first report on monitoring PSP evolution in optical fibres.