Abstract We study learning of a matching model for response selection in retrieval-based dialogue systems. The problem is equally important with designing the architecture of a model, but is less explored in existing literature. To learn a robust matching model from noisy training data, we propose a general co-teaching framework with three specific teaching strategies that cover both teaching with loss functions and teaching with data curriculum. Under the framework, we simultaneously learn two matching models with independent training sets. In each iteration, one model transfers the knowledge learned from its training set to the other model, and at the same time receives the guide from the other model on how to overcome noise in training. Through being both a teacher and a student, the two models learn from each other and get improved together. Evaluation results on two public data sets indicate that the proposed learning approach can generally and significantly improve the performance of existing matching models