Objective: This review examines the evidence from head-to-head randomised controlled trials addressing whether the efficacy of cognitive-behavioural therapy for anxiety disorders, obsessive-compulsive disorder and post-traumatic stress disorders in adults delivered by computer or online (computer- and Internet-delivered cognitive-behavioural therapy) is not inferior to in-person cognitive-behavioural therapy for reducing levels of symptoms and producing clinically significant gains at post-treatment and at follow-up. A supplementary aim is to examine the evidence for severity as a moderator of the relative efficacy of computer- and Internet-delivered cognitive-behavioural therapy and in-person cognitive-behavioural therapy. Method: PubMed, PsycINFO, Embase and Cochrane database of randomised trials were searched for randomised controlled trials of cognitive-behavioural therapy for these disorders with at least an in-person cognitive-behavioural therapy and Internet or computer cognitive-behavioural therapy arm. Results: A total of 14 randomised controlled trials (9 Internet, 5 computer) of cognitive-behavioural therapy for social anxiety disorder, panic disorder and specific phobia and 3 reports of effect moderators were included. One study showed a low risk of bias when assessed against risk of bias criteria for non-inferiority trials. The remaining studies were assessed as high or unclear risk of bias. One study found that Internet-delivered cognitive-behavioural therapy was superior and non-inferior at post-treatment and follow-up to group in-person cognitive-behavioural therapy for social anxiety disorder. One study of Internet-delivered cognitive-behavioural therapy for panic disorder showed non-inferiority to individual in-person cognitive-behavioural therapy for responder status at post-treatment and one of Internet cognitive-behavioural therapy for panic disorder for symptom severity at follow-up. Other comparisons (22 Internet, 13 computer) and for estimates pooled for Internet cognitive-behavioural therapy for social anxiety disorder, Internet cognitive-behavioural therapy for panic disorder and computer-delivered cognitive-behavioural therapy studies did not support non-inferiority. Evidence of effect moderation by severity and co-morbidity was mixed. Conclusion: There is limited evidence from randomised controlled trials which supports claims that computer- or Internet-delivered cognitive-behavioural therapy for anxiety disorders is not inferior to in-person delivery. Randomised controlled trials properly designed to test non-inferiority are needed before conclusions about the relative benefits of in-person and Internet- and computer-delivered cognitive-behavioural therapy can be made. Prospero: CRD420180961655-6