The purpose of this note is to provide an approximation for the generalized bootstrapped empirical process achieving the rate in [38]. The proof is based on the same arguments used in [36]. As a conséquence, we establish an approximation of the bootstrapped kernel distribution estimation. Purthermore, our results are applied to two-sample testing procedures as well as to change-point problems. We end with establishing strong approximations of the bootstrapped empirical process when the parameters are estimated.