We study both theoretically and experimentally the dynamic tunability of the magnetic resonance of a single nonlinear split-ring resonator with varactor diode at microwave frequencies. We demonstrate different tuning regimes with and without an inductive coil in parallel with the varactor. We show that the coil changes the sign of the nonlinearity and eliminates the memory effect caused by charge accumulation across the varactor. In addition, at higher powers the nonlinear response of the split-ring resonator becomes multivalued, paving a way for creating bistable tunable metamaterials.