On minimal $\omega$-composition non-$\frak H$-formations

Let $\frak{H}$ be some class of groups. A formation $\frak{F}$ is called a minimal $\tau$-closed $\omega$-composition non-$\frak{H}$-formation [1] if $\frak{F}\nsubseteq\frak{H}$ but $\frak{F}_1\subseteq\frak{H}$ for all proper $\tau$-closed $\omega$-composition subformations $\frak{F}_1$ of $\frak{F}$. In this paper we describe the minimal $\tau$-closed $\omega$-composition non-$\frak{H}$-formations, where $\frak H$ is a 2-multiply local formation and $\tau$ is a subgroup functor such that for any group $G$ all subgroups from $\tau(G)$ are subnormal in $G$.