In this paper, we study the postural behaviour of two categories of people: Post-CVA subjects suffering from cerebrovascular accident syndromes and healthy individuals under several levels of anterior–posterior and medial–lateral sinusoidal disturbances (0.1–0.5 Hz). These perturbations were produced from an omnidirectional platform called Isiskate. Afterwards, we have quantified seventy postural parameters, they were combined of linear stabilometric parameters and non-linear time dependent stochastic parameters using stabilogram diffusion analysis and some spectral attributes using power spectral density. The aim of our analysis is to reduce data dimensionality using principal component analysis (PCA). Furthermore, we proposed a new PCA-related criterion named: criterion of contribution in order to evaluate the contribution of every variable in the resulted system structure, and thus to eliminate the redundant postural characteristics. Afterwards, we highlighted some interesting distinctive parameters. The selected parameters were used thereafter in comparison between the studied groups. Finally, we created a classification model using support vector machines to distinguish stroke patients. Our proposed techniques help in understanding the human postural dynamics and facilitate the diagnosis of pathologies related to equilibrium which can be used to improve the rehabilitation services.