Recently, with the advances in digital signal processing, compression of biomedical signals has received great attention for telemedicine applications. In this paper, an adaptive transform coding-based method for compression of respiratory and swallowing sounds is proposed. Using special characteristics of respiratory sounds, the recorded signals are divided into stationary and nonstationary portions, and two different bit allocation methods (BAMs) are designed for each portion. The method was applied to the data of 12 subjects and its performance in terms of overall signal-to-noise ratio (SNR) values was calculated at different bit rates. The performance of different quantizers was also considered and the sensitivity of the quantizers to initial conditions has been alleviated. In addition, the fuzzy clustering method was examined for classifying the signal into different numbers of clusters and investigating the performance of the adaptive BAM with increasing the number of classes. Furthermore, the effects of assigning different numbers of bits for encoding stationary and nonstationary portions of the signal were studied. The adaptive BAM with variable number of bits was found to improve the SNR values of the fixed BAM by 5 dB. Last, the possibility of removing the training part for finding the parameters of adaptive BAMs for each individual was investigated. The results indicate that it is possible to use a predefined set of BAMs for all subjects and remove the training part completely. Moreover, the method is fast enough to be implemented for real-time application.