Novel nonlinear predictors are studied for nonlinear systems with delayed measurements without assuming globally Lipschitz conditions or a known predictor map but requiring instead bounded state trajectories. The delay is constant and known. These nonlinear predictors consists of a series of dynamic filters that generate estimates of the state vector (and its maximum magnitude) at different delayed time instants which differ from one another by a small fraction of the overall delay. (C) 2015 Elsevier Ltd. All rights reserved.