We consider the problem of function of state plus unknown input estimation of a linear time-invariant system using only the measured outputs. Two reduced-order input estimators built upon a state functional observer are proposed. The first is an extension of a state/input estimator, while the second is based on adaptive observer design technique. The proposed estimator can be designed under less restrictive conditions than those of the previous work, and unlike some of the past studies the proposed observer can be designed for certain nonminimum phase systems. (C) 2003 Elsevier Ltd. All rights reserved.