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. A group of young adults and 10−12‐year old children were either trained on an adaptive multiple‐session response inhibition task or performed a control activity. The trained participants from both age groups displayed significant improvements during training and positive transfer to a similar inhibition task. Reliable, albeit short‐lived, transfer effects were only found for the children, specifically to working memory updating and task‐switching tasks.