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Environment perception in autonomous driving vehicles often heavily relies on deep neural networks (DNNs), which are subject to domain shifts, leading to a significantly decreased performance during DNN deployment. Usually, this problem is addressed by unsupervised domain adaptation (UDA) approaches trained either simultaneously on source and target domain datasets or even source-free only on target data in an offline fashion. In this work, we further expand a source-free UDA approach to a continual and therefore online-capable UDA on a single-image basis for semantic segmentation. Accordingly, our method only requires the pre-trained model from the supplier (trained in the source domain) and the current (unlabeled target domain) camera image. Our method Continual BatchNorm Adaptation (CBNA) modifies the source domain statistics in the batch normalization layers, using target domain images in an unsupervised fashion, which yields consistent performance improvements during inference. Thereby, in contrast to existing works, our approach can be applied to improve a DNN continuously on a single-image basis during deployment without access to source data, without algorithmic delay, and nearly without computational overhead. We show the consistent effectiveness of our method across a wide variety of source/target domain settings for semantic segmentation. Code is available at https://github.com/ifnspaml/CBNA.