Learning generalizable representation and classifier for class-imbalanced data is challenging for data-driven deep models. Most studies attempt to re-balance the data distribution, which is prone to overfitting on tail classes and underfitting on head classes. In this work, we propose Dual Compensation Residual Networks to better fit both tail and head classes. First, we propose dual Feature Compensation Module (FCM) and Logit Compensation Module (LCM) to alleviate the overfitting issue. The design of these two modules is based on the observation: an important factor causing overfitting is that there is severe feature drift between training and test data on tail classes. In details, the test features of a tail category tend to drift towards feature cloud of multiple similar head categories. So FCM estimates a multi-mode feature drift direction for each tail category and compensate for it. Furthermore, LCM translates the deterministic feature drift vector estimated by FCM along intra-class variations, so as to cover a larger effective compensation space, thereby better fitting the test features. Second, we propose a Residual Balanced Multi-Proxies Classifier (RBMC) to alleviate the under-fitting issue. Motivated by the observation that re-balancing strategy hinders the classifier from learning sufficient head knowledge and eventually causes underfitting, RBMC utilizes uniform learning with a residual path to facilitate classifier learning. Comprehensive experiments on Long-tailed and Class-Incremental benchmarks validate the efficacy of our method.