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In part 2, fast motion estimation algorithm with name Fast Multigrid Pattern Search (FMPS) for H.264 is proposed. The proposed method showed that it works about 4 times faster. The peak signal to noise ratio in different video sequences shows better and worse results than characteristics of known algorithms (up to 3.75%) so it requires further investigation. Also, part 2 deals with the fast motion estimation algorithms for interframe encoding in the video data H.26 /HEVC standard. A new adaptive algorithm has been offered based on the analysis of the advantages and disadvantages of existing algorithms. The algorithm is called fast test zone search algorithm and includes the traditional test zone search algorithm (TZS) and the hierarchical search MP (Hierarchical Search or Mean Pyramid). The considered and proposed motion estimation algorithms have been tested in several video sequences using Microsoft Visual Studio software. The terms for algorithms evaluating were: the video sequence quality criterion (by PSNR), bitrate and encoding time. The proposed method showed that it works about 4 times faster. The average loss of the RD curve value (PSNR versus bitrate) is up to 4% in all.