This study investigated the development of prospective memory using tasks based on the prefrontal-lobe model. Three groups each of 30 children, adolescents, and young adults were compared on prospective-memory performance using ongoing tasks with two levels of cognitive demand (low and high), and two levels of importance (unstressed and stressed) of remembering prospective cues. The Self-Ordered Pointing Task (SOPT), Stroop Color Word Interference Test, and Tower of London were also used to assess relationships between prospective memory and prefrontal-lobe functions. The children remembered fewer prospective cues than either the adolescents or adults, but the adolescents and adults remembered equally well. This trend increased significantly as the cognitive demand of the ongoing tasks increased. However, stressing or not stressing the importance of remembering made no difference to prospective-memory performance. Performance on the SOPT and Stroop Colour Word Interference predicted performance on the high- but not on the low-demand condition. These findings implicate the maturation of the brain's prefrontal region in the development of prospective memory.