Let $\{ V_{ i}\}_{ i=1}^{ n}$ be a finite family of closed subsets of a plane or a sphere $S^{ 2}$, each homeomorphic to the two-dimensional disk. In this paper we discuss the question how the boundary of connected components of a complement $\rr^{ 2} \setminus \bigcup_{ i=1}^{ n} V_{ i}$ (accordingly, $S^{ 2} \setminus \bigcup_{ i=1}^{ n} V_{ i}$) is arranged. It appears, if a set $\bigcup_{ i=1}^{ n} \Int V_{ i}$ is connected, that the boundary $\partial W$ of every connected component $W$ of the set $\rr^{ 2} \setminus \bigcup_{ i=1}^{ n} V_{ i}$ (accordingly, $S^{ 2} \setminus \bigcup_{ i=1}^{ n} V_{ i}$) is homeomorphic to a circle.
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