The physics of nonlinear dynamics has been studied in detail in macroscopic mechanical systems like the driven classical pendulum. By now, it is possible to build mechanical devices on the nanometer scale with eigenfrequencies on the order of several 100 MHz. In this work, we want to present how to machine such nanomechanical resonators out of silicon-on-insulator wafers and how to operate them in the nonlinear regime in order to investigate higher-order mechanical mixing at radio frequencies. The nonlinear response then is compared in detail to nth-order perturbation theory and nonperturbative numerical calculations.