This thesis covers research into joint oversampled subband audio processing and coding. The integration of subband audio processing and subband audio coding is beneficial for audio devices such as wireless digital hearing aids where processing delay and computational resources are constraints on the application. In this thesis we first evaluate an oversampled single-sideband (SSB) filter bank which has real-valued subband signals for signal coding and is free from aliasing cancellation constraints which can impede subband audio processing performance. Oversampled subband predictive coding systems are then developed for this filter bank. Noise predictive, signal predictive and composite predictive coding methods are evaluated and shown to provide consistent improvements in SNR. The oversampled subband predictors are also evaluated using a simple adaptive quantizer and real-world audio signals. These results demonstrate that improvements are possible with little additional computation, but that the design must carefully consider stability issues in the predictive coders.