Here, we demonstrate the fabrication of single-layer MoS2 mechanical resonators. The fabricated resonators have fundamental resonance frequencies in the order of 10 MHz to 30 MHz (depending on their geometry) and their quality factor is about ~55 at room temperature in vacuum. The dynamical properties clearly indicate that monolayer MoS2 membranes are in the membrane limit (i.e., tension dominated), in contrast to their thicker counterparts, which behave as plates. We also demonstrate clear signatures of nonlinear behaviour of our atomically thin membranes, thus providing a starting point for future investigations on the nonlinear dynamics of monolayer nanomechanical resonators.