Three phase induction motors are widely used in industrial processes and condition monitoring of these motors is especially important. Broken rotor bars, eccentricity and bearing faults are the most common types of faults of induction motors. Stator current and/or vibration signals are mostly preferred for the monitoring and detection of these faults. Fourier Transform (FT) based detection methods analyse the characteristic harmonic components of stator current and vibration signals for feature extraction. Several types of simultaneous faults of induction motors may produce characteristic harmonic components at the same frequency (with varying amplitudes). Therefore, detection of multiple faults is more difficult than detection of a single fault with FT based diagnosis methods. This paper proposes an alternative approach to detect simultaneous multiple faults including broken rotor bars, static eccentricity and outer/inner-race bearing faults by analysing stator current and vibration signals. The proposed method uses Hilbert envelope analysis with a Normalized Least Mean Square (NLSM) adaptive filter. The results are experimentally verified under 25%, 50%, 75%, 100% load conditions.