We study sequential learning of interventions in environments that are nonstationary, but where the nonstationarity is constrained by a causal graph. Specifically, we introduce Adversarial Causal Bandit, which is an environment, where the relation between actions and intermediate variables follows a known causal mechanism, whereas the relation between intermediate variables and outcomes can be adversarial. Therefore, we significantly relax the assumptions on the loss generation compared to the commonly studied (stochastic) Causal Bandit. We also introduce a Causal Self-Bounding condition, which allows to interpolate between adversarial and stochastic versions of Causal Bandits and characterize intermediate regimes such as Corrupted Causal Bandits. For the interest of comparison we derive fast-rate (logarithmic) regret bounds for existing CUCB and CTS in the stationary regime and experimentally show that these are, however, prone to failure when the environment is not stationary. As a remedy, we propose a family of Causal Tsallis-INF algorithms, which uses causal graph information in a novel way. For that family we prove best-of-both-worlds property: the algorithm exhibits worst case robustness to deviations from the stationary regime and achieves fast-rate otherwise (expressed in terms of context gaps that can be arbitrarily larger than action gaps).