  Let $G$ be a strictly pseudoconvex domain in $\mathbb{C}^2$ with
$C^\infty$-smooth boundary $\partial G$. Let $S$ be a 2-dimensional sphere
embedded into $\partial G$. Denote by $\mathcal{E}$ the set of all complex
points on $S$. We study how the structure of the set $\mathcal{E}$ depends on
the smoothness of $S$
