This paper focuses on the model reduction of nonstationary linear parameter-varying (LPV) systems. We provide an explicit method for the model reduction of such systems, along with an a priori error bound, which amounts to the generalization of balanced truncation to this nonstationary LPV setting. Our work is motivated by the desire to analyze and control nonlinear systems along prespecified trajectories. The journal version of this paper can be found at http://www.ews.uiuc.edu/-farhood/.