Background: In general, Internet-delivered cognitive behavior therapy (iCBT) produces significant reductions in child and adolescent anxiety, but a proportion of participants continue to show clinical levels of anxiety after treatment. It is important to identify demographic, clinical, and family factors that predict who is most likely to benefit from iCBT in order to better tailor treatment to individual needs. Methods: Participants were 175 young people (7-18 years) with an anxiety disorder, and at least one of their parents, who completed an iCBT intervention with minimal therapist support. Multilevel modeling (MLM) examined predictors of response to iCBT as measured by the slope for changes in the primary outcome measures of child-and parent-reported anxiety scores, from pretreatment, to 12-weeks, 6-month, and 12-month follow-ups, controlling for pretreatment total clinician severity ratings of all anxiety diagnoses. Results: Child age, gender, father age, parental education, parental mental health, parenting style, and family adaptability and cohesion did not significantly predict changes in anxiety in the multivariate analyses. For child-reported anxiety, greater reductions were predicted by a separation anxiety disorder diagnosis (SEP) and elevated depression, with lower reductions predicted by poor couple relationship quality. For parent-reported child anxiety, greater reductions were predicted by higher pretreatment total CSRs, SEP, and lower family income, with lower reductions for children of older mothers. Irrespective of these predictors of change, children in general showed reductions in anxiety to within the normal range. Conclusions: Overall, children responded well to iCBT irrespective of the demographic, clinical, and family factors examined here. Poor couple relationship quality and older mother age were risk factors for less positive response to iCBT in terms of reductions in anxiety symptoms although still to within the normal range.