Response inhibition is crucial for mental and physical health but studies assessing the trainability of this type of inhibition are rare. Thirty-nine children aged 10-12 years and 46 adults aged 18-24 years were assigned to an adaptive go/no-go inhibition training condition or an active control condition. Transfer of training effects to performance on tasks assessing response inhibition, interference control, working memory updating, task-switching, and non-verbal fluid intelligence were assessed during 3- and 6-month follow-up sessions and/or an immediate post-training session. Significant training improvements and positive transfer effects to a similar response inhibition task with other stimuli were observed for both children and adults. Reliable albeit short-lived transfer effects were only found for the children, specifically to working memory updating and task switching. These results suggest some potential for response-inhibition training programs to enhance aspects of cognitive functioning in children but not adults.