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In this work, we present five new versions of the fast Newton transversal filter algorithm (FNTF). The first algorithm is based on a simple modification of the filtering part, by introducing a scalar accelerator parameter. The second algorithm is based on the use of a block filtering technique to actualize the local filter coefficients. The third algorithm is a modification of the second algorithm by the use of the final filtering errors to actualize the filters coefficients. The fourth and the fifth algorithms are based respectively on the combination of features from the first algorithm with features of the second and third algorithms. These five new algorithms were proposed to improve the convergence speed of the original version of the FNTF algorithm for the identification of acoustic impulse responses, and to also improve their tracking ability when these systems vary in time. The different algorithms and their comparative results are presented.