The paper discusses a new, fully recursive approach to the adaptive modeling, forecasting and seasonal adjustment of nonstationary economic time-series. The procedure is based around a time variable parameter (TVP) version of the well known “component” or “structural” model. It employs a novel method of sequential spectral decomposition (SSD), based on recursive state-space smoothing, to decompose the series into a number of quasi-orthogonal components. This SSD procedure can be considered as a complete approach to the problem of model identification and estimation, or it can be used as a first step in maximum likelihood estimation. Finally, the paper illustrates the overall adaptive approach by considering a practical example of a UK unemployment series which exhibits marked nonstationarity caused by various economic factors.