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Measuring the center of pressure (CoP) for a subject positioned on a force plate is one of the most commonly used tools to investigate balance. Several studies have proven a significant degradation of the body’s stability after the age of 60. The conclusions, however, are based on a limited number of indicators and without systematic nonlinear analysis methods being used to evaluate the progression of CoP parameter values. Neither the change in CoP movement in subjects over 60 years of age nor the considerations of their body mass index (BMI) has been systematically evaluated by nonlinear methods so far. This study is based on one of the frequent methods for nonlinear evaluation – the Recurrent Quantification analysis. This article discusses the applicability of this method with regards to the evaluation of changes in postural stability of subjects over 60 years of age. Postural stability changes were evaluated using CoP motion and tested by the nonlinear method. For this research purpose, a group of 103 elderly women were selected and divided into age-respective groups of 60–69 years and 70–79 years old. Each age group was further divided into a subgroup of normal and overweight subjects according to their BMI. The following recurrent analysis parameters were employed in the evaluation of CoP motion in medial-lateral and anterior-posterior directions: determinism (DET), laminarity (LAM) and trapping time (TT). The results of the Wilcoxon test revealed a statistically significant difference between the values in parameters for the different age groups of overweight subjects almost in all the cases. Conversely, statistically significant differences between age groups rarely occurred in a subgroup of subjects with a normal BMI.