Since primary droplets in atomization processes are produced with initial surface distortions, the energy carried by surface modes can be converted to other modes by nonlinear interactions, a conversion that provides a possible mechanism of secondary droplet generation (secondary atomization). In this study some nonlinear aspects of drop-shape oscillations have been investigated. The natural frequency of droplet oscillations increases with increasing amplitude of excitation for oblate-biased deformations what is in contradiction with the classical linearized theory of oscillations. By larger amplitudes of oscillation a new phenomenon has been observed. Jump phenomenon, known from non-linear mechanics took place by linear sweeping of the amplitude-modulated frequency around the resonant linear frequency of a droplet. Such jumps occurs suddenly and in very abrupt manner. Jumps in amplitude cause either damping or amplification of droplet oscillations. The amplification may become very violent and is possibly responsible for sudden break-up of droplets. Such jumps are unpredictable, depend on initial droplet deformation and have extremely small time scales; typically a few ms.