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This paper proposes some methods for estimating the order of nonlinear systems having non-integer order. First, the stability of time-varying order systems is studied. Afterward, the multivariable systems with time-varying incommensurate order are studied and an estimation scheme is proposed to approximate the order. In the next step, considering the pseudo-states of a system to be unknown, an order/pseudo-state estimator is designed for a category of nonlinear systems. It is shown that the method is extendible to form order/pseudo-state estimators for other classes of nonlinear systems using other traditional nonlinear observers. One of the advantages of the proposed methods is that a compact time interval is enough to guarantee bounded estimation error., Competing Interests: Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2021 ISA. Published by Elsevier Ltd. All rights reserved.)