Abstract. The Madden–Julian oscillation (MJO) is the main controller of the weather in the tropics on intraseasonal timescales, and recent research provides evidence that the quasi-biennial oscillation (QBO) influences the MJO interannual variability. However, the physical mechanisms behind this interaction are not completely understood. Recent studies on the normal-mode structure of the MJO indicate the contribution of global-scale Kelvin and Rossby waves. In this study we test whether these MJO-related normal modes are affected by the QBO and stratospheric ozone. The partial directed coherence method was used and enabled us to probe the direction and frequency of the interactions. It was found that equatorial stratospheric ozone and stratospheric zonal winds are connected with the MJO at periods of 1–2 months and 1.5–2.5 years. We explore the role of normal-mode interactions behind the stratosphere–troposphere coupling by performing a linear regression between the MJO–QBO indices and the amplitudes of the normal modes of the atmosphere obtained by projections on a normal-mode basis using ERA-Interim reanalysis data. The MJO is dominated by symmetric Rossby modes but is also influenced by Kelvin and asymmetric Rossby modes. The QBO is mostly explained by westward-propagating inertio-gravity waves and asymmetric Rossby waves. We explore the previous results by identifying interactions between those modes and between the modes and the ozone concentration. In particular, westward inertio-gravity waves, associated with the QBO, influence the MJO on interannual timescales. MJO-related modes, such as Kelvin waves and Rossby waves with a symmetric wind structure with respect to the Equator, are shown to have significantly different dynamics during MJO events depending on the phase of the QBO.