This is a Phase 3, open-label, single-group, non-randomised, observational study of the safety and biochemical disease control of Infacort® in neonates, infants and children with AI who have completed study Infacort 003 (EudraCT number 2014-002265-30). All subjects who have satisfactorily completed study Infacort 003 will be offered the opportunity to participate in study Infacort 004 at or after their final visit of study Infacort 003. Subjects will receive the usual clinically-appropriate dose (since bioequivalence has been demonstrated with conventional hydrocortisone), as determined by the Investigator, which will be administered according to usual clinical practice - generally 3 or 4 times a day. Subjects can continue to be treated in this study until they meet the study withdrawal criteria, Infacort® is granted a marketing authorisation (and so is available commercially, which is expected within 2 years of initiation of this study), Infacort® is refused a marketing authorisation, or the Sponsor decides to discontinue the study.