This paper analyzes the numerical identifiability of the electrical parameters of induction machines. Formulations of the single and double-cage induction machine, with and without core-losses in both models, are developed. The impossibility of identifying all the parameters of these models when only external measurements (voltage, current, speed and torque) are used is shown. One proposed solution is the formulation of machine equations by using the minimum number of parameters (which are identifiable parameters). As an application example, the parameters of a double-cage induction machine are identified using steady-state measurements corresponding to different angular speeds.