Let K be an algebraic number eld and let (Gn) be a linear recurring sequence dened by Gn = 1 n 1 +P2(n) n 2 + +Pt(n) n t , where 1; 1; : : : ; t are non-zero elements of K and where Pi(x) 2 K(x) for i = 2; : : : ; t. Furthermore let f(z; x) 2 K(z; x) monic in x. In this paper we want to study the polynomial{exponential Diophantine equation f(Gn; x) = 0. We want to use a quantitative version of W. M. Schmidt's Subspace Theorem (due to J.-H. Evertse (8)) to calculate an upper bound for the number of solutions (n; x) under some additional assumptions.