There are established El Nino-Southern Oscillation (ENSO) and Quasi-biennial Oscillation (QBO) teleconnections to the extratropics that alter the strength of the polar vortex. Here, we demonstrate non-linearity in the stratospheric polar vortex response to ENSO and QBO combined, in climate model simulations and observational data. We show that the combined effect of El Nino and QBO easterly phase (QBO-E) on the polar vortex is greater than the linear combination of the individual responses to El Nino and QBO-E separately. Observations support the model results, despite a relatively small sample of observed cases. We propose that non-linearity in the teleconnection to ENSO and QBO is caused by the combined effects of an increase in wave driving from El Nino and more poleward propagation of wave activity during QBO-E. Our results have implications for extreme winters when both El Nino and QBO-E are active. Plain Language Summary The El Nino-Southern Oscillation (ENSO) describes cycles of warmer and cooler sea surface temperatures in the tropical Pacific Ocean. The Quasi-biennial Oscillation (QBO) is a cycle of alternating easterly and westerly winds in the tropical stratosphere, around 15-40 km above ground. Although these climate cycles occur in the tropics, their impacts are felt far outside the tropics. Both ENSO and QBO are known to affect the stratospheric polar vortex, a band of strong winds that encircle the Arctic in winter. Here, we use climate model experiments and observations to quantify the effects of ENSO and QBO on the polar vortex, when these factors occur alone and in combination. Warm ENSO conditions, known as El Nino, and the easterly QBO phase both cause the polar vortex to weaken. We show that the polar vortex weakens more when El Nino and QBO easterly occur together than would be expected by the sum of their individual effects. Our results are relevant to seasonal forecasting of winter weather over Europe and North America, as a weakened polar vortex is often followed by abnormally cold weather. Our results imply that cold winters are more likely when both El Nino and easterly QBO conditions occur together, such as in 2009/10.