A motor task that requires fine control of upper limb movements and a cognitive task that requires executive processing—first performing them separately and then concurrently—was performed by 18 young and 18 older adults. The motor task required participants to tap alternatively on two targets, the sizes of which varied systematically. The cognitive task required participants to generate a series of random numbers at fixed production rates. Participants' performance on the motor task decreased slightly from single- to concurrent-task condition, and the dual-task cost was age-independent. Older adults showed large cognitive dual-task costs as motor-control demands increased. Younger adults' cognitive performance was not affected by concurrent task demands. These results are discussed in light of the permeation model developed by Baltes and Lindenberger (1997). Practical implications and educational recommendations are presented.