We present a modern method used in nonlinear time series analysis to investigate the relation of two oscillating systems with respect to their phases, independently of their amplitudes. We study the difference of the phase dynamics between El Ni¿o/Southern Oscillation (ENSO) and the Indian Monsoon on inter-annual time scales. We identify distinct epochs, especially two intervals of phase coherence, 1886--1908 and 1964--1980, corroborating earlier findings from a new point of view. A significance test shows that the coherence is very unlikely to be the result of stochastic fluctuations. We also detect so far unknown periods of coupling which are invisible to linear methods. These findings suggest that the decreasing correlation during the last decades might be a typical epoch of the ENSO/Monsoon system having occurred repeatedly. The high time resolution of the method enables us to present an interpretation of how volcanic radiative forcing could cause the coupling.