We proposed and investigated novel methods for polarization demultiplexing using artificial neural networks (ANNs). It was shown that a three-layer ANN includes butterfly operations and has a polarization-demultiplexing capability. Our proposed cascaded construction of a butterflystructure of FIR filters and an ANN connecting x-and y-polarization components exhibited superior performance in terms of the polarizationdemultiplexing speed. By using the proposed method, optical nonlinearity can also be compensated for at the same time. We examined and compared the performance of the proposed methods by numerical simulations using 10-Gsymbol/s polarization multiplexed 16QAM optical signals.