Temporal shifts in phenology or vegetation period of plants are seen as indicators of global warming with potentially severe impacts on ecosystem functioning. In spite of increasing knowledge on drivers, it is of utmost importance to disentangle the relationship between air temperatures, phenological events, potential temporal lags (phase shifts) and time scale for certain plant species. Assessing the phase shifts as well as the scale-dependent relationship between temperature and vegetation phenology requires the development of a nonlinear temporal model. Therefore, we use wavelet analysis and present a framework for identifying scale-dependent cross-phase coupling of bivariate time series. It allows the calculation of (a) scale-dependent decompositions of time series, (b) phase shifts of seasonal components in relation to the annual cycle, and (c) inter-annual phase differences between seasonal phases of different time series. The model is applied to air temperature data and remote sensing phenology data of a beech forest in Germany. Our study reveals that certain seasonal changes in amplitude and phase with respect to the normal annual rhythm of temperature and beech phenology are coupled time-delayed components, which are characterized by a time shift of about one year.