Summary Background Respiratory disease may cause profound hypoxaemia during flight. Previously derived linear equations poorly predict the need for supplemental oxygen during air travel. The current gold standard assessment is the hypoxic challenge test (HCT). Recent guidelines recommend HCT is performed for those patients with SpO2 < 95% at sea level. The HCT protocol is a costly and time consuming investigation. Methods Retrospective clinical and HCT data from 138 patients were applied to previous linear equations to assess predictive value. Novel non-linear predictive models (NLMs) were constructed from these data. The linear equations and the NLMs were then applied prospectively to 44 patients undergoing HCT. Results Overall, 39% of historic patients had a positive HCT (PaO2N2 <50 mmHg). Existing linear equations varied in sensitivity (52–87%) and specificity (40–74%) at predicting positive HCT results. Seven novel NLMs (NLM1 to NLM7) were developed from the historic dataset. All NLMs predicted PaO2N2 more accurately than the original linear equations when tested prospectively. The best fit was observed using NLM2 which uses PaO2RA and PaCO2RA as input terms. The NLMs are applicable to a broad range of conditions. Conclusions The novel NLMs represent a low cost option for the prediction of significant hypoxia during flight and perform better than SpO2 in identifying those patients who require more formal assessment with HCT.