Background: Oesophagectomy is an operation with a high risk of postoperative complications. The aim of this single-centre retrospective study was to apply machine-learning methods to predict complications (Clavien-Dindo grade IIIa or higher) and specific adverse events. Methods: Patients with resectable adenocarcinoma or squamous cell carcinoma of the oesophagus and gastro-oesophageal junction who underwent Ivor Lewis oesophagectomy between 2016 and 2021 were included. The tested algorithms were logistic regression after recursive feature elimination, random forest, k-nearest neighbour, support vector machine, and neural network. The algorithms were also compared with a current risk score (the Cologne risk score). Results: 457 patients had Clavien-Dindo grade IIIa or higher complications (52.9 per cent) versus 407 patients with Clavien-Dindo grade 0, I, or II complications (47.1 per cent). After 3-fold imputation and 3-fold cross-validation, the overall accuracies were: logistic regression after recursive feature elimination, 0.528; random forest, 0.535; k-nearest neighbour, 0.491; support vector machine, 0.511; neural network, 0.688; and Cologne risk score, 0.510. For medical complications, the results were: logistic regression after recursive feature elimination, 0.688; random forest, 0.664; k-nearest neighbour, 0.673; support vector machine, 0.681; neural network, 0.692; and Cologne risk score, 0.650. For surgical complications, the results were: logistic regression after recursive feature elimination, 0.621; random forest, 0.617; k-nearest neighbour, 0.620; support vector machine, 0.634; neural network, 0.667; and Cologne risk score, 0.624. The calculated area under the curve of the neural network was 0.672 for Clavien-Dindo grade IIIa or higher, 0.695 for medical complications, and 0.653 for surgical complications. Conclusion: The neural network scored the highest accuracies compared with all of the other models for the prediction of postoperative complications after oesophagectomy.