Abstract The paper concerns inclusions of Bavrin families of complex valued functions which are hololomorphic in bounded complete n-circular domains G ⊂ C n $\mathcal{G} \subset \mathbb{C}^{n}$ and fulfil some geometric conditions. Such families X G $\mathcal{X}_{G}$ were applied later to research some families of locally biholomorphic mappings in C n $\mathbb{C}^{n}$ . (see for instance, J. A. Pfaltzgraff and T. J Suffridge, P. Liczberski, I. Graham and G. Kohr, H. Hamada, T. Honda, G. Kohr). Some results for functions of such families X G $\mathcal{X}_{G}$ were obtained by [BAVRIN, I. I.: A Class of Regular Bounded Functions in the Case of Several Complex Variables and Extreme Problems in That Class, Moskov Obl. Ped. Inst., Moscow, 1976 (Russian)], [DŁUGOSZ, R.: Embedding theorems for holomorphic functions of several complex variables, J. Appl. Anal. 19 (2013), 153--165], [DŁ UGOSZ, R.—LEŚ, E.: Embedding theorems and extremal problems for holomorphic functions on circular domains of C n $\mathbb{C}^{n}$ , Complex Var. Elliptic Equ. 59 (2014), 883--899], [LEŚ-BOMBA, E.—LICZBERSKI, P.: New properties of some families of holomorphic functions of several complex variables, Demonstratio Math. 42 (2009), 491--503], et al..