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: Does the robustness of cross-lingual transfer on XTREME-R improve when intermediate-task training incorporates typologically diverse non-English languages versus monolingual English datasets?Autonomous synthesis report generated by Assignee Research. Tribunal consensus score: 9.3/10.