Continuous assimilation of altimetric sea level differences from the simulated Geosat exact repeat mission (ERM) into a three-layer, quasi-geostrophic, eddy-resolving numerical ocean box model at mid-latitude was conducted using the method of optimal interpolation (Lorenc, 1981). In the linear portion of the model domain, the assimilation of simulated Geosat altimetric sea level differences constrained the detectable periods/wavelengths of mesoscale eddy activity, within the limits of accuracy of the initialization, nearly indefinitely. However, in the nonlinear portion of the model domain, the constraint of these otherwise detectable periods/wavelengths degraded with time from the point of initialization, due to the influence of nonlinear processes and aliasing upon the assimilation process. Hence reinitialization at period intervals was indicated. The Nyquist wavelength of mesoscale eddy activity that could be constrained by the simulated Geosat ERM (i.e., 140-km track separation at mid-latitudes, 45-km sampling interval along track) in the nonlinear portion of the model domain was determined to be the track separation, and not the sampling interval along track; hence in both the linear and nonlinear portions of the model domain, wavelengths greater than 280 km were constrained, but wavelengths shorter than 280 km were not. Therefore decreasing the track separation in future satellite altimeter strategies will be the only way that smaller wavelength scales of mesoscale eddy activity can be detected. This should also increase the capability of the model to constrain the nowcast of the mesoscale eddy activity in the nonlinear portions of the model domain beyond initialization. It was established that the constraint of mesoscale eddy activity in the middle and lower layer stream function fields of the model was similar to that in the upper layer stream function field, responding to the same Nyquist criteria. ¿ American Geophysical Union 1990