We consider algebra - differential equations of the normal form and Cauchy problem  as follows:
where t ∈[0, T], Y : G ⊂ R n → R m, F : G ⊂ R n → R n - m, x(t) ∈ R m, z(t) ∈ R n - m .
Combined numerical methods for solution (1): implicit Euiler´s scheme with simple iterations and implicit Runge -Kutta´s scheme with Newton´s iterations are presented. It is shown convergence and exact numerical solutions.
Asymptotic properties of the both combined methods are discussed. We also give examples in which the numerical and the exact solutions are compared.
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The work is submitted to the IV Scientific International Conference "Basic research", Italy, October, 11-18, 2008, came to the editorial office on 19.08.2008.