Аннотация:Let $F$ be a free group generated by a finite alphabet$A$. Let $N_1$ (resp., $N_2$) be the normal closure of a finitenon-empty symmetrized set $R_1$ (resp., $R_2$) of elementsin $F$.In \cite{okConj}, one obtained the conditions sufficient for the solvability of the conjugacy problem in the group $F/{N_1\cap N_2}$.The present paper is devoted to the solvability of the multiple conjugacy problem in $F/{N_1\cap N_2}$.In particular, we get that if $R_1\cup R_2$ satisfies the small cancellation condition $C'(\frac{1}{6})$, then the multiple conjugacy problem is solvable in $F/{N_1\cap N_2}$.https://doi.org/10.1007/s10958-022-05848-2