Steganography is the art of hiding information in ways that prevent its detection. A message in cipher text may arouse suspicion while an invisible message will not. Digital steganography uses a host data or message, known as a “container” or “cover” to hide another data or message called “secret” in it. An audio in audio steganography system had been proposed in this thesis in order to embed a secret audio data in another cover audio data. In this system, the secret data is first transformed using wavelet transform and then the resultant coefficients have to be coded using one of the three coding methods (fixed length encoding method, S-shift coding method and hybrid coding method). The next stage in this system is the embedding stage where the output of coding stage (a stream of bits) is embedded in the cover data. Three embedding methods were implemented in the proposed system (least significant bit insertion in wavelet transform domain, two least bits insertion in time domain with recovery technique and hiding in audible parts). A modified fidelity criteria were derived by adding some modifications to the standard fidelity criteria to be more precise for audio and the modified criteria are called (modified Mean Square Error, modified Signal to Noise Ratio and modified Peak Signal to Noise Ratio) and they also used through the system testing stage. All of the fidelity criteria obtained in the tests have indicates good results for PSNR and its modified version (50 dB). The reconstructed data is exactly the same as secret data if the integer wavelet transform is used before the coding stage while a small unrecognizable error may done when the Haar wavelet transform is used before the coding stage.