Model reduction by moment-matching relies upon the availability of the so-called moment. If the system is nonlinear, the computation of moments depends on an underlying specific invariance equation, which can be difficult or impossible to solve. This article presents four technical contributions related to the theory of moment matching: first, we identify a connection between moment-based theory and weighted residual methods. Second, we exploit this relation to provide an approximation technique for the computation of nonlinear moments. Third, we extend the defini- tion of nonlinear moment to the case in which the generator is described in explicit form. Finally, we provide an approximation technique to compute the moments in this scenario. The results are illustrated by means of two examples.