Multi-annual oscillations have been observed in measured atmospheric data. These oscillations are also present in general circulation models. This is the case even if the model boundary conditions with respect to solar cycle, sea surface temperature, and trace gas variability are kept constant. The present analysis contains temperature oscillations with periods from below 5 up to more than 200 years in an altitude range from the Earth's surface to the lower thermosphere (110 km). The periods are quite robust as they are found to be the same in different model calculations and in atmospheric measurements. The oscillations show vertical profiles with special structures of amplitudes and phases. They form layers of high or low amplitudes that are a few dozen kilometres wide. Within the layers the data are correlated. Adjacent layers are anticorrelated. A vertical displacement mechanism is indicated with displacement heights of a few 100 m. Vertical profiles of amplitudes and phases of the various oscillation periods as well as their displacement heights are surprisingly similar. The oscillations are related to the thermal and dynamical structure of the middle atmosphere. These results are from latitudes and longitudes in central Europe.