On the basis of the adjoint approach, different types of oscillatory mechanisms of instabilities in two-layer systems are investigated. It is shown that for Marangoni convection oscillatory instability may become the only possible mechanism of instability in the system. The evolution of non-linear regimes of oscillations is analysed. For different aspect ratios different kinds of bifurcations, including period doubling bifurcation and transition to the steady state through a homoclinic bifurcation, are observed. The combined action of Marangoni and Rayleigh mechanisms of instabilities can lead to oscillations even in the case where "pure" Marangoni and "pure" Rayleigh instabilities are stationary. It is shown that the presence of the surface active agents may lead to the specific types of oscillations : the frequency of oscillations is proportional to the wave number in the long-wave limit. Oscillatory Marangoni convection in systems with a deformable interface is investigated.