Let \(\{X^ 0_ i\), \(i\geq 1\}\) be a sequence of i.i.d. rv’s with continuous df \(F^ 0(t)\) and survival function \(S^ 0(t)\). Let \(\{\gamma_{m,n}(t)\}\) and \(\{\beta_{m,n}(t)\}\) be the bootstrapped product-limit process and the corresponding process, respectively. The authors proved mainly that under some conditions there exists a sequence of Wiener processes \(\{\hat W_ n(t)\), \(t\geq 0\}^{\infty}_{n=1}\) such that \[ P\{\sup_{-\infty <t\leq T}| \gamma_{m,n}(t)-S^ 0(t)\hat W_ m(d(t))| \geq A\quad n^{-1/4}(\log n)^{5/4}\}\leq Bn^{-\epsilon} \] for all \(\epsilon >0\), and with additional conditions \[ \sup_{-\infty <t\leq T}| \gamma_{m,n}(t)-S^ 0(t)\hat W_ m(d(t))| /q(F^ 0(t))\to^{P}0. \] These results enable to use easily the bootstrapped product-limit estimator in practice.