Let $(M_j,g_j(t),x_j)$ be a sequence of pointed complete Ricci flows on smooth $n$-manifolds defined for $t\in(a,b)$, where $0\in(a,b)$. Assume that for every compact interval $J\subset(a,b)$ there is a constant $C(J)$ such that
Then a subsequence converges smoothly in the pointed Cheeger-Gromov sense to a complete pointed Ricci flow $(M_\infty,g_\infty(t),x_\infty)$ on $(a,b)$.