Brute-force implementation of the extended Kalman (EK) filter in realistic ocean models is not possible because of its prohibitive cost. Different degraded forms of the EK filter, which basically reduce the dimension of the system through some kind of projection onto a low dimensional subspace, have been proposed (Cane et al. 1996; Dee 1990; Fukumori and Malanotte-Rizzoli 1995b; Hoang et al. 1997). The goal of this paper is to study the usefulness of the evolution in time of these reduced state spaces. This is based on the comparison, both from the theoretical and practical points of view, of the singular evolutive extended Kalman (SEEK) filter introduced by Pham et al. (1997), and the reduced-order extended Kalman (ROEK) filter introduced by Cane et al. (1996). To reduce the cost of the ROEK filter, we further approximate the nonlinear dynamics of the system by a first order autoregressive stochastic model. The assimilation results of twin experiments, which we have conducted in a realistic setting of the OPA model in the tropical Pacific ocean, seem to indicate that the evolution of the reduced state space is beneficial during the model unstable periods, where the reduced space may not well represent the variability of the model.