Nonlinear systems models the dynamics of an oscillatory system under the action of an external periodic force with frequency. Examples of such systems are electric nonlinear circuits with an alternating electomotive force, a pendulum under the action of a periodically varying torque, Josephson's superconducting junctions in the case of an alternating excitation current, and so on. This chapter examines the dynamics of a weakly dissipative oscillator with a small nonlinearity arising under the action of a small harmonic force. It also analyzes a possible form of the resonance curves determined by the forced oscillation of a nonlinear oscillator. The nonlinearity substantially modifies the dynamics of a nonautonomous oscillator. The simultaneous existence of two regimes of forced oscillations becomes possible in the system.