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Referring Expression Comprehension (REC) aims to localize an image region of a given object described by a natural-language expression. While promising performance has been demonstrated, existing REC algorithms make a strong assumption that training data feeding into a model are given upfront, which degrades its practicality for real-world scenarios. In this paper, we propose Continual Referring Expression Comprehension (CREC), a new setting for REC, where a model is learning on a stream of incoming tasks. In order to continuously improve the model on sequential tasks without forgetting prior learned knowledge and without repeatedly re-training from a scratch, we propose an effective baseline method named Dual Modular Memorization (DMM), which alleviates the problem of catastrophic forgetting by two memorization modules: Implicit-Memory and Explicit-Memory. Specifically, the former module aims to constrain drastic changes to important parameters learned on old tasks when learning a new