Rotor fault diagnosis of induction machines is commonly realized through Motor Current Signature Analysis (MCSA), i.e., by classical spectrum analysis of the input currents. However, this technique may fail in the case of outer cage damage of double cage induction motors, due to the small current circulation in the rated operating conditions. The situation is more complicated under time-varying conditions, where the typical Rotor Fault Frequency Components (RFFCs), which appear in the phase current spectrum of faulty motors, are spread in a bandwidth proportional to the speed variation and are difficult to detect accurately. A new diagnosis method based on the combined use of Double-Frequency Sliding (DFS) and Discrete Wavelet Transform (DWT) is proposed here for the analysis of the stator phase current. A experimental study on a copper-made double cage separate end ring rotor shows the validity of the proposed approach, leading to an effective diagnosis procedure for fault detection in double cage motors under time-varying conditions.