This study analyzes the magnetic field wave characteristics of a wireless power transfer (WPT) system from a time-varying view in the nonradiative near field. Phenomena of both forward and backward traveling waves were found. These wave phenomena refer to magnetoinductive waves (MIWs) according to the findings in this study and MIW theory and characteristics. A traditional MIW only appears in the MIW waveguide, which is always constructed by many parallel coils. However, this study analyzed MIWs in a two-coil WPT system, proving that MIWs exist not only in a multi-coil system but also in a basic two-coil system. The velocity of MIWs, a kind of a phase velocity, was calculated. An approximate equation for evaluating wave velocity is proposed. Furthermore, the MIWs in the two-coil WPT system were extended into a more general situation. In this general situation, two separated standing waves were set, and a traveling wave was generated by those two standing waves. The result explains the mechanisms of MIWs in a general situation from a time-varying view. Lastly, a simulation was conducted to verify the accuracy of the study. The results demonstrated that MIWs exist, and the approximate equation is correct. This study presents a novel view on the mechanisms of the WPT system from a wave view.