Modern satellite altimetry provides an ideal tool for studying sea level variations. Simulated altimeter data are used to implement a new assimilation technique in an oceanic regional model. This variational data assimilation method is the dual formulation of the usual four-dimensional variational algorithm. That dual formulation can take model error into account at a computational cost which is similar to the cost incurred in the exact model case. Another feature of this original technique is to minimize the dual objective function under weak constraint in the observation space <Bennett, 1992; Amodei, 1995>. The assimilation algorithm is used in the Miami Isopycnic-Coordinate Ocean Model (MICOM). This oceanic adiabatic primitive equation model describes an idealized flow with four immiscible layers. Our purpose is twofold. First, we show the links between primal and dual methods. We implement them in academic cases and we discuss the behavior of both algorithms. Second, we examine the efficiency of the dual technique in assimilating altimeter data of the Gulf Stream circulation. This work presents the first implementation of variational assimilation methods with the MICOM model that includes an external mode. Operator splitting is used to advance that mode with larger steps than those used for internal modes. We have numerically shown the possibility to solve a weak constraint problem without additional computational cost compared with the strong constraint variational algorithm. We present experiments for different time periods to assess the ability of the assimilation scheme to transfer the surface information downward to the deep flows. Numerical results show that our variational algorithm applied with the MICOM model produces a realistic estimation from a 2-month assimilation period. ¿ 2001 American Geophysical Union