Software for use in aviation requires certi cation. This cer- ti cation is based on a safety argument. These arguments are formed of claims that are linked to evidence about the system. Adaptive sys- tems are a grey area within the current certi cation guidelines (DO-178 document). Safety cases (sometimes called safety arguments) link claims and evidence in support of an overall safety argument. This paper argues that it is rational to have an adaptive safety argument for an adaptive system. This is illustrated by considering an adaptive controller that uses Explanation-Based Learning (EBL) to generate both control laws and a safety argument, represented using Goal-Structuring Notation. An adaptive safety argument, when coupled with analytical tools, could be used to form the adaptive portion of an otherwise standards-based cer- ti cation argument. If the rest of the argument holds then the argument should hold for any state where the adaptive safety cases remain valid.