The problem of the continuous-time H-infinity fixed-lag smoothing over the infinite horizon is studied. The first solution to the problem is derived in terms of one algebraic Riccati equation of the same dimension as in the filtering case and the mechanism by which the performance improvements with respect to the H-infinity filtering occur is clarified. It is shown that the H-infinity smoother exploits the information preview in an "H-2 manner". (C) 2003 Elsevier Ltd. All rights reserved.