processes but it is a consequence of unbounded region occupied by the oscillating system. The latter naturally leads to the energy loss due to the wave emission (for example, gravity waves).

In this paper we would like to show that the quasi-normal modes are not the peculiarities of the gravitational problems only. Actually they appear, in a natural way, when considering the oscillating systems unbounded in space. The necessary condition for emergence of such modes is imposing the radiation condition at spatial infinity on the field functions. It is this condition that leads to the characteristic behaviour of the quasi-normal modes, namely, these solutions to the relevant equations exponentially decay in time when $t\to
\infty$ and simultaneously they exponentially rise at spatial infinity $r\to \infty$. An interesting and physically motivated example is provided here by the oscillations of electromagnetic field connected with a compact dielectric sphere placed in unrestricted homogeneous media with a different refraction index or in vacuum. Taking here the formal limit $\varepsilon \to \infty$ one passes to a perfectly conducting sphere ($\varepsilon $ is the refraction index of the sphere material). In this case the quasi-normal modes describing the electromagnetic oscillations outside the sphere are tractable analytically. 