The mathematical model for the potentiostatic work of CP-based electrochemical sensors and biosensors, used for the detection of two strong organic acids with the common “acid” functional group (using the example of –SO3H group), was developed and analyzed by the using of linear stability theory and bifurcation analysis. The steady-state stability conditions, corresponding to the better response, were developed. The presence of oscillatory and monotonic instabilities was also confirmed.