This paper describes sequence alignment algorithms of nucleotide sequences. There are described pairwise alignment algorithms using database search or dynamic programming. Then in the paper is description of dynamic programming for multiple sequences and algorithm that builds phylogenetic trees. At the end of the first part of the paper is the description of technology FPGA. In the second part that is more practical is described implemntation of the choosen one algorithm. This part includes also examples of some multiple alignments.