We show how to include absorption effects in a normal incidence state-space model of a layered media system. Two models are discussed: a convolutional state-space model and a differential-delay state-space model. Extensive results are presented for the former model, whereas only formulative results are presented for the latter.For the convolutional state-space model we develop absorption impulse responses in closed form for Gaussian and exponential absorption operators. Simulation results demonstrate that this model has the desired low-pass filtering effect expected of a system with absorption losses.The differential-delay state-space model does not appear to have been applied before in the context of seismic modeling. We suggest it as a useful model.