The simple postural task of quiet standing, which requires minimal attentional resources, is generally paired with cognitive activity. Competition for attentional resources is a consequence of simultaneously performing balance tasks and cognitive tasks, and impairment of attentional resource allocation with aging leads to increased risks of fall. We investigated age-related changes in posture control during dual task performance, using a paradigm that crossed a static (quiet standing) and a dynamic (keeping balance on a translational force plate) postural task and cognitive tasks of low demand (mental arithmetic) and high demand (spatial memory). Postural performance was analyzed through center-of-pressure displacements using both statistical (body sway area/sway velocity) and nonlinear (wavelet transform) methods in three age groups (younger, middle-aged, and older healthy participants). Results showed that 1) the nonlinear analysis method was more sensitive than the traditional approach in distinguishing performance between age groups, a result that explains discrepancies in the dual-task literature; 2) dual-tasking costs were dependent on both postural task difficulty and cognitive task complexity, corroborating previous investigations; 3) younger adults improved their postural performance during dual-tasking, but older adults lowered their performance; 4) balance recovery strategies in the dynamic postural task appeared to differ in younger versus older adults. Together, our findings on dual-tasking can be interpreted within the conceptual frame of task prioritization: shifting attention away from postural task automates posture control in the younger adults, whereas prioritization of postural task and selection of compensatory strategy are the main characteristics of posture control in the older population.