Our objective is to demonstrate the applicability of adaptive wavelets for speech applications. In particular, we discuss two applications, namely, classification of unvoiced sounds and speaker identification. First, a method to classify unvoiced sounds using adaptive wavelets, which would help in developing a unified algorithm to classify phonemes (speech sounds), is described. Next, the applicability of adaptive wavelets to identify speakers using very short speech data (one pitch period) is exhibited. The described text-independent phoneme based speaker identification algorithm identifies a speaker by first modeling phonemes and then by clustering all the phonemes belonging to the same speaker into one class. For both applications, we use feed-forward neural network architecture. We demonstrate the performance of both unvoiced sounds classifier and speaker identification algorithms by using representative real speech examples.