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The statistical structure of DNA-sequences is of a great interest to molecular biology, genetics and the theory of evolution (see Chen and others, GIW-99, 1999, Aktulga and others, EURASIP J. of Bioinformatics and Systems Biology, 2007, Li, Computers and Chemistry , 1997). One of the approaches is a sequence modeling using Markov processes of different orders, and further statistical estimation of their parameters (see Simons and others, JSPI , 2005). In this paper we use firstly the test for the serial independence from Ryabko, Astola (Stat. Methodology, 2006) to estimate the ldquomemoryrdquo (or connectivity) of genetic texts and secondly we apply the homogeneity test for solving the DNA-based problem connected to the phylogenetic system of various organisms.