Age-related decline in executive functions and postural control due to degenerative processes in the central nervous system have been related to increased fall-risk in old age. Many studies have shown cognitive-postural dual-task interference in old adults, but research on the role of specific executive functions in this context has just begun. In this study, we addressed the question whether postural control is impaired depending on the coordination of concurrent response-selection processes related to the compatibility of input and output modality mappings as compared to impairments related to working-memory load in the comparison of cognitive dual and single tasks. Specifically, we measured total center of pressure (CoP) displacements in healthy female participants aged 19–30 and 66–84 years while they performed different versions of a spatial one-back working memory task during semi-tandem stance on an unstable surface (i.e., balance pad) while standing on a force plate. The specific working-memory tasks comprised: (i) modality compatible single tasks (i.e., visual-manual or auditory-vocal tasks), (ii) modality compatible dual tasks (i.e., visual-manual and auditory-vocal tasks), (iii) modality incompatible single tasks (i.e., visual-vocal or auditory-manual tasks), and (iv) modality incompatible dual tasks (i.e., visual-vocal and auditory-manual tasks). In addition, participants performed the same tasks while sitting. As expected from previous research, old adults showed generally impaired performance under high working-memory load (i.e., dual vs. single one-back task). In addition, modality compatibility affected one-back performance in dual-task but not in single-task conditions with strikingly pronounced impairments in old adults. Notably, the modality incompatible dual task also resulted in a selective increase in total CoP displacements compared to the modality compatible dual task in the old but not in the young participants. These results suggest that in addition to effects of working-memory load, processes related to simultaneously overcoming special linkages between input- and output modalities interfere with postural control in old but not in young female adults. Our preliminary data provide further evidence for the involvement of cognitive control processes in postural tasks.