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In this study, the normal form method which had been previously applied to three of the Sprott systems is applied to three other Sprott systems with a different eigenvalue structure of their linearized parts. It is seen that the normal form expansion can also represent these systems successfully for a longer time than expected from a perturbative method. Altough the normal form expansion is a local method it gives information about nonlocal characteristics such as possible zero Liapunov exponents of the system via approximately conserved quantities.