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Today, adaptive algorithms represent one of the most frequently used computational tools for the processing of digital speech signals. This work investigates and analyzes the properties of adaptive algorithms in speech communication applications where rigorous conditions apply, such as noise and echo cancelation. Like other theses in this field do, it tries to tackle the ever-lasting problem of computational complexity vs. rate of convergence. It introduces some new adaptive methods that stem from the existing algorithms as well as a novel concept which has been entitled OSS.