In this paper we introduce the notion of Dynamic Generalized Controllability and Observability functions for nonlinear systems. These functions are called dynamic and generalized since they make use of additional states (dynamic extension) and are such that partial differential inequalities are solved in place of equations. The presence of the dynamic extension permits the construction of classes of canonical controllability and observability functions without relying on the solution of any partial differential equation or inequality. The effectiveness of the proposed concept is validated by means of two applications: the model reduction problem via balancing and the sensor deployment problem in a continuous stirred tank reactor (CSTR). (C) 2014 Elsevier Ltd. All rights reserved.