We applied motion theory to robot audition to improve the inadequate performance. Motions are critical for overcoming the ambiguity and sparseness of information obtained by two microphones. To realise this, we first designed a sound source localisation system integrated with cross-power spectrum phase (CSP) analysis and an EM algorithm. The CSP of sound signals obtained with only two microphones was used to localise the sound source without having to measure impulse response data. The expectation-maximisation (EM) algorithm helped the system to cope with several moving sound sources and reduce localisation errors. We then proposed a way of constructing a database for moving sounds to evaluate binaural sound source localisation. We evaluated our sound localisation method using artificial moving sounds and confirmed that it could effectively localise moving sounds slower than 1.125 rad/s. Consequently, we solved the problem of distinguishing whether sounds were coming from the front or rear by rotating and/or tipping the robot's head that was equipped with only two microphones. Our system was applied to a humanoid robot called SIG2, and we confirmed its ability to localise sounds over the entire azimuth range as the success rates for sound localisation in the front and rear areas were 97.6% and 75.6% respectively.