Extensive studies are available that analyse time series of carbon dioxide and water flux measurements of FLUXNET sites over many years and link these results to climate change such as changes in atmospheric carbon dioxide concentration, air temperature and growing season length and other factors. Many of the sites show trends to a larger carbon uptake. Here we analyse time series of net ecosystem exchange, gross primary production, respiration, and evapotranspiration of four forest sites with particularly long measurement periods of about 20 years. The regular trends shown are interrupted by periods with higher or lower increases of carbon uptake. These breakpoints can be of very different origin and include forest decline, increased vegetation period, drought effects, heat waves, and changes in site heterogeneity. The influence of such breakpoints should be included in long-term studies of land-atmosphere exchange processes.