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We address the problem of incremental semantic segmentation (ISS) recognizing novel object/stuff categories continually without forgetting previous ones that have been learned. The catastrophic forgetting problem is particularly severe in ISS, since pixel-level ground-truth labels are available only for the novel categories at training time. To address the problem, regularization-based methods exploit probability calibration techniques to learn semantic information from unlabeled pixels. While such techniques are effective, there is still a lack of theoretical understanding of them. Replay-based methods propose to memorize a small set of images for previous categories. They achieve state-of-the-art performance at the cost of large memory footprint. We propose in this paper a novel ISS method, dubbed ALIFE, that provides a better compromise between accuracy and efficiency. To this end, we first show an in-depth analysis on the calibration techniques to better understand the effects on ISS. Based on this, we then introduce an adaptive logit regularizer (ALI) that enables our model to better learn new categories, while retaining knowledge for previous ones. We also present a feature replay scheme that memorizes features, instead of images directly, in order to reduce memory requirements significantly. Since a feature extractor is changed continually, memorized features should also be updated at every incremental stage. To handle this, we introduce category-specific rotation matrices updating the features for each category separately. We demonstrate the effectiveness of our approach with extensive experiments on standard ISS benchmarks, and show that our method achieves a better trade-off in terms of accuracy and efficiency.