In this talk we will introduce a new formalism to calculate nonlinear oscillations of fluids based on non-self-adjoint operators. The formalism is very intuitive, based on Eulerian description of perturbations and can be seen as an alternative to the standard Lagrangian approach used in the theory of nonlinear stellar pulsations. First we will review basic properties of nonlinear oscillations of systems having a single degree of freedom such as springs and pendulums and outline the method of multiple scales. We then move to continuous systems and outline our method. Finally, we apply it to nonlinear g-mode oscillations of thin accretion disks.