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Abstract.Mityagin posed the problem, whether complemented subspaces of nuclear infinite type power series spaces have a basis. A related more general question was asked by Pelczynski. It is well known for a complemented subspace £ of a nuclear infinite type power series space, that its diametral dimension can be represented by AE = AAoo(q) for a suitable sequence a with a, > \n(j + 1). In this article we prove the existence of a basis for E in case that aj > j and sup -^ < oo .It was shown by Mityagin, that complemented subspaces of nuclear finite type power series spaces always have a basis, and he asked, whether the same is valid for infinite type (cf. [3,4,5]). Dubinsky and Vogt [2] obtained a positive solution for some nuclear power series spaces Aoo(a), namely they assumed that the set of all finite limit points of {^-: i, j € N} is bounded. Results for some other special cases are stated below. Pelczynski [6] posed the more general problem, whether complemented subspaces of nuclear Fréchet spaces with basis again have a basis. Both problems are open up to now.Every complemented subspace E of a nuclear infinite type power series space has the same diametral dimension as a power series space A^ja) for a suitable sequence a with a >ln(y'-f-l) (cf. Terzioglu [8]). Considering isomorphisms between spaces of analytic functions Zaharjuta [15] conjectured that E has a basis for stable a (this means sup ^ < oo ). This will be proved in the present note in case a > /. Other positive solutions have been obtained if one of the three following assumptions is satisfied:(1) Aoo(a) is a complemented subspace of E (cf. Vogt [10]).(2) There is a tame projection onto E (cf. Dubinsky/Vogt [2]). (3) E is isomorphic to E ® E (cf. Wagner [14], see also [11]). The present proof uses result no. 1 of Vogt [10]. The main tool is the construction of a basis and of a projection in E by a permuted Gram-Schmidt orthonormalization.