The aim of this study was to investigate how additional cognitive tasks (Stroop test and counting backwards task) influence young adults' ability to generate appropriate postural responses while standing on a continuously oscillating platform. Twenty young adults (25.95 ± 2.97 years) stood on a moving platform which was translated in the anterior–posterior direction at three different frequencies (0.10, 0.25 and 0.50 Hz) in three dual‐task conditions (counting backwards task, a Stroop task or no additional cognitive task). Postural muscle onset latencies and tonic activity levels of the leg muscles were measured through surface electromyography; the number of steps taken and cognitive errors made were recorded. Results showed no significant differences in muscle activity between dual and single‐tasking conditions nor between the two dual tasking conditions. Cognitive errors were made in the counting backwards task but not the Stroop task. A frequency effect was identified with participants showing greater tonic activity in rectus femoris (p = 0.012), gastrocnemius medialis (p = 0.016) and bicep femoris (p = 0.043) at 0.5 Hz, as well as earlier muscle activation in tibialis anterior, gastrocnemius medialis and bicep femoris (p < 0.001) at 0.50 Hz. Transition and steady state muscle onset latencies were only significantly different for gastrocnemius medialis at 0.25 Hz (p = 0.001). Dual tasking did not seem to influence anticipatory postural adjustments in young adults; however, perturbation intensities did. The differences observed in the number of cognitive errors made could be indicative of the regional cortical activations and overlapping demand for resources interfering with balance control, though cortical activation was not recorded. Future research should include detailed cognitive behavior, including cortical activations and task reaction times to better understand the allocation of attentional resources during perturbed balance dual tasking.