If $C(n,1)$ denotes a simple $n$-cycle $v_1\to v_2\to\dots\to v_n\to v_1$ with an additional arc $v_jv_{j+i-1}$, for some $f\in\{1,2,\dots,n\}$ and $3\leq i\leq n-1$ it is proved that every strong $n$-tournament $T_n$ contains copies of $C(n,[(n+2)/2])$ and $C(n,n-2)$ for each $n$ $(n\geq4)$.