The notion of automatic group recently has been extended to semigroups and the basic properties of this new class of semigroups have been established by \textit{C. M. Campbell}, \textit{E. F. Robertson}, \textit{N. Ruškuc} and \textit{R. M. Thomas} [Theor. Comput. Sci. 250, No. 1-2, 365-391 (2001; Zbl 0987.20033)]. Given a finite alphabet \(A\), the author denotes by \(A^+\) the free semigroup generated by \(A\) consisting of finite sequences of elements of \(A\) under the concatenation, and by \(A^*\) the free monoid generated by \(A\) consisting of \(A^+\) together with the empty word \(\varepsilon\). Let the set \(A(2,\$)=((A\cup\{\$\})\times(A\cup\{\$\}))\setminus\{\$,\$\}\), where \(\$\) is a symbol not in \(A\). The function \(\delta_A\colon A^*\times A^*\to A(2,\$)^*\) is defined by \[ (a_1\cdots a_m,b_1\cdots b_n)\delta_A=\begin{cases}\varepsilon\quad &\text{if }0=m=n,\\ (a_1,b_1)\cdots(a_m,b_m)\quad &\text{if }0n\geq 0.\end{cases} \] Let \(S\) be a semigroup and \(A\) a finite generating set for \(S\) with respect to \(\psi\colon A^+\to S\). The pair \((A,L)\) is an automatic structure for \(S\) (with respect to \(\psi\)) if the following three properties hold: (1) \(L\) is a regular subset of \(A^+\) and \(L\psi=S\); (2) \(L_==\{(\alpha,\beta):\alpha,\beta\in L,\;\alpha=\beta\}\delta_A\) is regular in \(A(2,\$)^+\); (3) \(L_a=\{(\alpha,\beta):\alpha,\beta\in L,\ \alpha a=\beta\}\delta_A\) is regular in \(A(2,\$)^+\) for each \(a\in A\). A semigroup is automatic if it has an automatic structure. The main result is the following theorem. Let \(S\) be a free product of finitely many semigroups \(S=S_1*\cdots*S_n*T_1\cdots*T_m\), where \(T_1,\dots,T_m\) are free semigroups on finite sets \(Y_1,\dots,Y_m\), respectively. Let \(H=(t_1,\dots,t_l)\) be a subsemigroup of \(S\), where \(t_1,\dots,t_l\in S\setminus(S_1\cup\cdots\cup S_n)\). Then \(H\) is an automatic semigroup.