\indent a rigorous convergence theory for galerkin methods for a model helmholtz problem in $r^{d}, d=1,2,3,$ is presented. general conditions on the approximation properties of the approximation space are stated that ensure quasi-optimality of the method. as an application of the general theory, a full error analysis of the classical hp-version of the finite element method (hp-fem) is presented where the dependence on the mesh width $h$, the approximation order $p$, and the wave number $k$ is given explicitly. in particular, it is shown that quasi-optimality is obtained under the conditions that $kh/p$ is sufficiently small and the polynomial degree $p$ is at least $o(log k)$. this result improves existing stability conditions substantially.