This paper investigates,moving horizon state estimation (MHSE) within a,bounded-error context for continuous-time systems. Verified integration of the non-linear ordinary differential equations used as system equation is achieved with interval Taylor expansions. In addition, interval constraint propagation techniques are used in order to reduce the pessimism due to interval arithmetic. The new MHSE method is illustrated with a bio-process system, for several lengths of the time horizon: (c) 2004 Elsevier Ltd. All rights reserved.