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This paper discusses the use of partial state observations in the construction of reduced order models based on proper orthogonal decompositions (POD). A main motivation for this work lies in the observation that reductions of the state dimension of large scale nonlinear and time-varying models hardly enhances the computational speed of these models. It is shown that information from output variables or sampled state information can be used in an efficient manner to accelerate computation speed in reduced order models while allowing state recovery properties in an exact or approximate sense.