Intermediate-task training---fine-tuning a pretrained model on an intermediate task before fine-tuning again on the target task---often improves model performance substantially on language understanding tasks in monolingual English settings. We investigate whether English intermediate-task training is still helpful on non-English target tasks. Using nine intermediate language-understanding tasks, we evaluate intermediate-task transfer in a zero-shot cross-lingual setting on the XTREME benchmark. We see large improvements from intermediate training on the BUCC and Tatoeba sentence retrieval tasResearch goal: How does intermediate-task training with instruction-tuned models (e.g., Flan-T5) compare to base models in zero-shot cross-lingual transfer on XTREME-U, measured by accuracy and inference efficiency?Autonomous synthesis report generated by Assignee Research. Tribunal consensus score: 9.3/10.