This paper is an ELITR system submission for the non-native speech translation task at IWSLT 2020. We describe systems for offline ASR, real-time ASR, and our cascaded approach to offline SLT and real-time SLT. We select our primary candidates from a pool of pre-existing systems, develop a new end-to-end general ASR system, and a hybrid ASR trained on non-native speech. The provided small validation set prevents us from carrying out a complex validation, but we submit all the unselected candidates for contrastive evaluation on the test set.