In this work an efficient approach for a-posteriori error estimation for POD-DEIM reduced nonlinear dynamical systems is introduced. The considered nonlinear systems may also include time and parameter-affine linear terms as well as parametrically dependent inputs and outputs. The reduction process involves a Galerkin projection of the full system and approximation of the system's nonlinearity by the DEIM method [Chaturantabut & Sorensen (2010)]. The proposed a-posteriori error estimator can be efficiently decomposed in an offline/online fashion and is obtained by a one dimensional auxiliary ODE during reduced simulations. Key elements for efficient online computation are partial similarity transformations and matrix DEIM approximations of the nonlinearity Jacobians. The theoretical results are illustrated by application to an unsteady Burgers equation and a cell apoptosis model.