The classical \(n\)-point Gaussian quadrature rule is exact whenever it is applied to a linear combination of the functions \(x^0, x^1, \ldots, x^{2n-1}\). If we generalize this basis to the form \(x^{\lambda_0}, x^{\lambda_1}, \ldots, x^{\lambda_{2n-1}}\) with real numbers \(\lambda_0 < \lambda_1 < \cdots < \lambda_{2n-1}\) (a so-called Müntz system), we can still carry over the main elements of the theory, but the standard methods used for the explicit construction of the weights and nodes do not work any more. The paper under review presents an algorithm that solves this problem. A number of numerical examples underline the practicability of the method.